OP11 Abstracts - Society for Industrial and Applied ... · 72 OP11 Abstracts certain loads. We present the implementation of the opti-mal positioning of active components within a

70 OP11 Abstracts

IP1

Sparse Optimization

Many computational problems of recent interest can beformulated as optimization problems that contain an un-derlying objective together with regularization terms thatpromote a particular type of structure in the solution.Since a commonly desired property is that the vector ofunknowns should have relatively few nonzeros (a “sparsevector’), the term “sparse optimization’ is used as a broadlabel for the area. These problems have arisen in machinelearning, image processing, compressed sensing, and sev-eral other fields. This talk surveys several applicationsthat can be formulated and solved as sparse optimizationproblems, highlighting the novel ways in which algorithmshave been assembled from a wide variety of optimizationtechniques, old and new.

Stephen WrightUniversity of WisconsinDept. of Computer [email protected]

IP2

Optimizing Radiation Therapy - Past Accomplish-ments and Future Challenges

Optimization has found a successful and broad applicationin intensity-modulated radiation therapy (IMRT). We willbriefly review the standard model of IMRT optimization.There is still a lot of space for improvement in IMRT andelsewhere in radiation therapy: 1. Optimization of theirradiation geometry including multiple fixed beams anddynamic arcs. 2. The adaptation (re-optimization) of thetreatment during the course of treatment. 3. The han-dling of motion and uncertainties, particularly in protontherapy, and 4. The direct optimization of treatment out-come rather than physical (dosimetric) surrogates of it. Ageneral challenge is that physicians often cannot provideclear mathematical objectives and strict constraints. In-stead, they pursue an I know it when I see it approach. Wetry to address this issue through interactive multi-criteriaoptimization.

Thomas BortfeldMassachusetts General Hospital and Harvard MedicalSchoolDepartment of Radiation [email protected]

IP3

On Some Optimal Control Problems of Electro-magnetic Fields

In this survey, a sequence of optimal control problems forsystems of partial differential equations of increasing com-plexity is discussed. The audience is guided step by stepfrom an academic heating problem to fairly complex con-trol problems of induction heating. While the first prob-lem is modeled by the Poission equation, the last one isrelated to industrial applications. It includes equations forheat conduction, heat radiation, and Maxwell equationsmodeling induction heating. To introduce into main prin-ciples of PDE control, the talk begins with a simplifiedoptimal control problem for a linear elliptic equation withbox constraints on the control function. It can be inter-preted as a heating problem. Next, nonlinear local andnonlocal radiation boundary conditions are considered andthe geometry of the computational domain will be more

general. Moreover, box constraints on the state functionare also admitted. Later, the model is improved by in-cluding Maxwell equations for induction heating and stateconstraints on the generated temperature. Also the com-pletion of the model by Navier-Stokes equations in a melt isbriefly mentioned. For these problems, the well-posednessof the underlying systems of PDEs and the principal formof optimality conditions are sketched. Numerical examplesillustrate the theory, justify certain simplifications and andmotivate the necessity of more complex models. Finally,ongoing research on applications to industrial processes ofcrystal growth is briefly addressed.

Fredi TroltzschTechnische Universitat, [email protected]

IP4

Matrix Optimization: Searching Between the Firstand Second Order Methods

During the last two decades, matrix optimization prob-lems (MOPs) have undergone rapid developments due totheir wide applications as well as their mathematical ele-gance. In the early days, second order methods, in par-ticular the interior point methods (IPMs), seemed to bea natural choice for solving MOPs. This choice has beenperfectly justified over the years by the success of usingIPMs to solve small and medium sized semi-definite pro-gramming (SDP) problems. On the other hand, since ateach iteration the memory requirement and the computa-tional cost for second order methods grow too fast withthe number of constraints and the matrix dimensions inMOPs, second order methods have recently become lesspopular. The current trend is to apply first order methodsto MOPs. This comes no surprise as first order methodsnormally need less computational cost at each iteration.To say the least while first order methods can often run forsome iterations even for large scale problems, the secondorder methods may fail even at the first iteration. However,for many MOPs the overall cost of first order methods forobtaining a reasonably good solution is often prohibitive,if possible at all. To break this deadlock, we need to con-struct algorithms that possess two desirable properties: 1)at each iteration the computational cost is affordable; and2) the convergence speed is fast but may not be as fastas second order methods (no free lunch). In this talk, byusing least squares correlation matrix and SDP problemsas examples we demonstrate how these two properties canbe potentially achieved simultaneously. Variational anal-ysis, in particular semi-smooth analysis, will be empha-sized and inexact proximal point algorithms (PPAs) will berecommended for solving large scale symmetric and non-symmetric MOPs.

Defeng SunDept of MathematicsNational University of [email protected]

IP5

Replacing Spectral Techniques for Expander Ratio,Normalized Cut and Conductance by Combinato-rial Flow Algorithms

We address challenging problems in clustering, partition-ing and imaging including the normalized cut problem,graph expander, Cheeger constant problem and conduc-tance problem. These have traditionally been solved using

OP11 Abstracts 71

the “spectral technique”. These problems are formulatedhere as a quadratic ratio (Raleigh) with discrete constraintsand a single sum constraint. The spectral method solves arelaxation that omits the discreteness constraints. A newrelaxation, that omits the sum constraint, is shown to besolvable in strongly polynomial time. It is shown, via anexperimental study, that the results of the combinatorialalgorithm often improve dramatically on the quality of theresults of the spectral method in image segmentation andimage denoising instances.

Dorit HochbaumIndustrial Engineering and Operations ResearchUniversity of California, [email protected]

IP6

Nonsmooth Optimization: Thinking Outside of theBlack Box

In many optimization problems, nonsmoothness appearsin a structured manner, because the objective function hassome special form. For example, in compressed sensing,regularized least square problems have composite objectivefunctions. Likewise, separable functions arise in large-scalestochastic or mixed-integer programming problems solvedby some decomposition technique. The last decade hasseen the advent of a new generation of bundle methods,capable of fully exploiting structured objective functions.Such information, transmitted via an oracle or black box,can be handled in a highly versatile manner, depending onhow much data is given by the black box. If certain first-order information is missing, it is possible to deal withinexactness very efficiently. But if some second-order in-formation is available, it is possible to mimic a Newtonalgorithm and converge rapidly. We outline basic ideasand computational questions, highlighting the main fea-tures and challenges in the area on application examples.

Claudia [email protected]

IP7

Nonlinear Integer Optimization: Incomputability,Computability and Computation

Within the realm of optimization, the Nonlinear IntegerOptimization problem is, in some sense, the mother of alldeterministic optimization problems. As such, in its mostgeneral form, it is hopelessly intractable. Yet, because ofits obviously broad scope, it has its allure. By lookingat structured yet broad subclasses, interesting and usefulresults emerge. I will present several results that expandon its intractability. Looking at these results optimisti-cally, we are guided toward directions that can be fruitfulfor positive results for theory and computation. I will gointo a lot of detail on combinatorial structures and types offunctions for which we have polynomial-time exact and ap-proximation algorithms. Finally, I will present the statusof some efforts to develop rather “general-purpose’ compu-tational tools (bearing in mind that the general problem isprovably intractable).

Jon LeeIBM T.J. Watson Research [email protected]

IP8

Title Not Available at Time of Publication

Abstract not available at time of publication.

Thomas F. ColemanThe Ophelia Lazaridis Research ChairUniversity of [email protected]

CP1

Chance-Constrained Second-Order Cone Program-ming: A Definition

Second-order cone programs (SOCPs) are class of con-vex optimization problems. Stochastic SOCPs have beendefined recently to handle uncertainty in data definingSOCPs. A prominent alternative for stochastic program-ming for handling uncertain data is chance constrainedprogramming (CCP). In this presentation, we introducean extension of CCPs termed chance-constrained second-order cone programs (CCSOCPs) for handling uncertaintyin data defining SOCPs. Some applications of this newparadigm of CCP will be described.

Baha M. Alzalg, Ari AriyawansaWashington State [email protected], [email protected]

CP1

On Semidefinite Programming Relaxations of Max-imum K-Section

We derive a semidefinite programming bound for max k-equipartition problem, which is, for k = 2, at least asstrong as the well-known bound by Frieze and Jerrum. Fork ≥ 3 this new bound dominates a bound of Karish andRendl [S.E. Karish, F. Rendl. Semidefinite Programmingand Graph Equipartition. In: Topics in Semidefinite andInterior-Point Methods, P.M. Pardalos and H. Wolkowicz,Eds., 1998.] The new bound coincides with a recent boundby De Klerk and Sotirov for the more general quadraticassignment problem.

Cristian DobreTiUniversity of GroningenGroningen, The [email protected]

Etienne De KlerkTilburg [email protected]

Dmitrii PasechnikNTU [email protected]

Renata SotirovTilburg [email protected]

CP1

Robust Design of Active Trusses Via Mixed IntegerSemidefinite Programming

This work is an extension of Ben-Tal and Nemirovskis ap-proach on Robust Truss Topology Design to active trusses.Active trusses may use active components to react on un-

72 OP11 Abstracts

certain loads. We present the implementation of the opti-mal positioning of active components within a semidefinitemodel for robust truss-topology design using binary vari-ables. Different robust approaches (polyhedral and ellip-soidal uncertainty sets), solution methods (e.g. cascadingtechniques, projection approaches) and numerical resultswill be presented.

Kai HabermehlTU Darmstadt, Department of MathematicsNonlinear [email protected]

Stefan UlbrichTechnische Universitaet DarmstadtFachbereich [email protected]

Sonja FriedrichTU Darmstadt, Department of MathematicsDiscrete [email protected]

CP1

Distributionally Robust Optimization and ItsTractable Approximations

We focus on a linear optimization problem with uncertain-ties, having expectations in the objective and in the set ofconstraints. We present a modular framework to obtain anapproximate solution to the problem that is distribution-ally robust and more flexible than the standard techniqueof using linear rules. We convert the uncertain linear pro-gram into a deterministic convex program by constructingdistributionally robust bounds on these expectations.

Melvyn SimNUS Business [email protected]

Joel GohStanford [email protected]

CP1

Attacking Molecular Conformation Problem bySDP

We present an improvement of the DISCO algorithm of Le-ung and Toh for molecular conformation. In the algorithm,the recursive steps recursively divide large group of atomsinto two overlapping subgroups until each subgroups is suf-ficient small. At that point, the graph realization problemsin the basis steps are solved via semidefinite programs. Af-ter which, the subgroups are stitched back together usingthe overlapping atoms, and the stitched configurations arerefined by a gradient decent method. We use chemical in-formation such as bond lengths and angles for atoms onthe backbone of a protein molecule to improve the robust-ness of the DISCO algorithm for computing the structureof a protein molecule given only a very sparse subset (20%)of inter-atomic distances that are less than 6Aand are cor-rupted by high level of noise. Tests on molecules taken fromthe Protein Data Bank show that our improved algorithmis able to reliably and efficiently reconstruct the conforma-tion of large molecules. For instance, a 6000-atom confor-mation problem is solved within an hour with an RMSD

of less than 1A.

Xingyuan FangPrinceton [email protected]

Kim-Chuan TohNational University of SingaporeDepartment of Mathematics and Singapore-MIT [email protected]

CP1

Optimization over the Doubly Nonnegative Cone

We often see that each element of the semidefinite relax-ation matrix is meant to be nonnegative. Such a matrix iscalled a doubly nonnegative matrix. In this talk, we willshow that the doubly nonnegative relaxation gives signif-icantly tight bounds for a class of quadratic assignmentproblems. We also provide some basic properties of thedoubly nonnegative cone aiming to develop new and effi-cient algorithms for solving the doubly nonnegative opti-mization problems.

Yasuaki MatsukawaGraduate School of Systems and Information EngineeringUniversity of [email protected]

Akiko YoshiseUniversity of Tsukubaraduate School of Systems and Information [email protected]

CP2

On Maximally Violated Cuts Obtained from a Ba-sis

Most cuts used in practice can be derived from a basis andare of the form αT x ≥ 1, where x is a vector of non-basicvariables and α ≥ 0. Such cuts are called maximally vio-lated wrt. a point x ≥ 0 if αT x = 0. In an earlier paperwe presented computational results for maximally violatedcuts derived from an optimal basis of the linear relaxation.In this talk we also consider pivoting and deriving maxi-mally violated cuts from alternative non-optimal bases.

Kent AndersenUniversity of [email protected]

CP2

A New Feasibility Pump-Like Heuristic for MixedInteger Problems

Mixed-Integer optimization represents a powerful tool formodeling many optimization problems arising from real-world applications. The Feasibility pump is a heuristic forfinding feasible solutions to mixed integer linear problems.In this work, we propose a new feasibility pump approachusing concave non differentiable penalty functions for mea-suring solution integrality. We present computational re-sults on general MILP problems from the MIPLIB libraryshowing the effectiveness of our approach.

Marianna De Santis, Stefano Lucidi, Francesco RinaldiUniversity of [email protected], [email protected],

OP11 Abstracts 73

[email protected]

CP2

A Traveling Salesman Problem with QuadraticCost Structure

We regard a traveling salesman problem with quadraticcost terms (QTSP) depending on any two successive arcsin the tour. This problem is motivated by an applicationin bioinformatics – the recognition of transcription factorbinding sites in gene regulation. It can also be used tosolve the angular-metric traveling salesman problem ap-pearing in connection with robotics and traveling sales-man problems with reload costs. For the linearized QTSPmodel we present a polyhedral study and investigate thecomputational complexity of the corresponding separationproblems. Using the new cuts, real world instances frombiology can be solved up to 80 cities in less than 13 min-utes. Random instances turn out to be difficult, but onthese semidefinite relaxations help to reduce the gap in theroot node significantly.

Anja Fischer, Christoph HelmbergChemnitz University of [email protected],[email protected]

CP2

A Novel Model: Planning, Scheduling and Re-source Allocation of Engineering Activities in Man-ufacturing Systems and Service Industries

This research deals with planning, scheduling and resourceallocation of activities in non-shop floor areas of manu-facturing systems and service industries. A mixed integerprogramming model and a decision support system was de-veloped, including operational features such as flexibilityof work force, legal restrictions on workload, and acces-sible capacities and resources. A real-life test, originatingfrom an industrial partner, shows the flexibility and the ro-bustness of the model by solving planning and schedulingproblems.

Yousef HooshmandInstitute for Product EngineeringUniversity of Duisburg-Essen, [email protected]

Amir HooshmandInstitute for Advanced StudyTechnical University of Munich, [email protected]

Dalibor DudicStuttgart [email protected]

CP2

New Continuous Reformulations for Zero-One Pro-gramming Problems

In this work, we study continuous reformulations of zero-one programming problems. We prove that, under suitableconditions, the optimal solutions of a zero-one program-ming problem can be obtained by solving a specific contin-uous problem. Furthermore, we develop a new feasibility-pump like approach for zero-one programming problems

based on the proposed reformulations, and we present com-putational results on binary MILP problems showing theusefulness of the approach.

Francesco Rinaldi, Marianna De SantisUniversity of [email protected], [email protected]

CP2

Orbital Branching for Quadratic Assignment Prob-lems of High Symmetry

Quadratic assignment problems are notoriously difficultto solve to optimality, and the difficulties are often com-pounded in instances exhibiting a high degree of symmetryamong decision variables. To address symmetry, we pro-pose an orbital-branching approach geared specially towardquadratic assignment problems.

Stephen E. WrightMiami UniversityDept of Math & [email protected]

CP3

Adjoint-Based Global Error Techniques for Inte-gration in Optimal Control Problems

Using the direct multiple shooting method to solve opti-mal control problems requires integrating dynamical sys-tems and generating sensitivity information for functionand derivative evaluation. To do this efficiently, discretiza-tion schemes should be chosen to balance accuracy require-ments for a successful optimization against computationaleffort. To this end we investigate global error techniquesbased on adjoint information. We present how this ad-joint information can efficiently be obtained from quanti-ties computed by backward differentiation of the integra-tion scheme in the case of variable-stepsize, variable-orderBDF methods.

Doerte Beigel

Interdisciplinary Center for Scientific Computing (IWR)Heidelberg [email protected]

Hans Georg BockIWR, University of [email protected]

Johannes SchloederIWR, University of Heidelberg, [email protected]

CP3

Symmetric Error Estimates for DiscontinuousTime Stepping Schemes for Optimal Control Prob-lems

A discontinuous Galerkin finite element method for an op-timal control problem having states constrained to linearand semi-linear parabolic PDE’s is examined. The schemesunder consideration are discontinuous in time but conform-ing in space. We present some results concerning error es-timates for the first order necessary conditions under min-imal regularity assumptions. The estimates are of sym-metric type and lead to optimal convergence rates under

74 OP11 Abstracts

suitable assumptions on the data.

Konstantinos ChrysafinosDepartment of MathematicsNational Technical University of Athens, [email protected]

CP3

Convex Optimization for Model Predictive Control

In this contribution, we describe algorithms and computa-tional performance of quadratic programming algorithmstailored for linear MPC with soft output constraints. Weconsider a primal active-set algorithm, a dual-active setalgorithm, and a primal-dual interior-point algorithm forsolution of convex QPs and tailor these algorithms forthe special structure of linear MPC with soft output con-straints. Linear MPC with soft output constraints is anattractive optimization model for control of uncertain lin-ear systems and systems with asymmetric penalty func-tions. However, the size of the decision variables growswith the number of soft output constraints and slack vari-ables introduced to shape the penalty function for the MPCproblem. The resulting convex QP for the linear MPC withsoft constraints easily becomes much larger than the equiv-alent linear MPC without soft output constraints. Due tothe real-time computational requirement off-the-shelf QPalgorithms are often too slow and efficient convex QP al-gorithms tailored for this problem are needed.

John B. JorgensenDTU InformaticsTechnical University of [email protected]

CP3

A Total Site Optimization Study for PlantwideControl

In order to develop control strategies for entire plants(plantwide control) and to jump over the lack of algorithmsthat is still present in this field we can apply total sitesteady-state optimization and then select the best controlstrategy. This paper is presenting a study of a total siteoptimization for a vacuum residue processing plant in or-der to maximize profit. The results will then be used as apriori information in the development of control strategiesfor the same plant.

Ionut Muntean, Andreea Savu, Gheorghe Lazea, MihailAbrudeanTechnical University of Cluj-Napoca, Faculty ofAutomationand Computer Science, Automation [email protected],[email protected], [email protected],[email protected]

CP3

Trajectory Planning and Task Allocation of Co-operating Vehicles Based on Discrete-ContinuousModeling and Optimization

Optimal task allocation and trajectory planning for coop-erating vehicles is characterized by complex multi-phasecontrol problems with tight coupling of discrete structureand continuous dynamics. Using hierarchical hybrid au-tomata and applying appropriate transformations, makesthe model accessible for mathematical optimization. In

particular, linear approximations are used for reasons ofefficiency and global optimality of the resulting mixed-integer linear problem. For benchmark scenarios and fornew problems numerical results are demonstrating real-time competitiveness as well as limitations.

Christian ReinlTechnische Universitat [email protected]

Oskar Von StrykDepartment of Computer ScienceTechnische Universitat [email protected]

CP3

Experiments of Automatic Differentiation inAerospace Applications

EADS Innovation Works, as research center of EADS, isinvolved in the development of inverse methods for trajec-tory tools. Two aerospace applications will be presentedwith a focus on inverse problem, optimal control and firstexperiments with automatic differentiation (AD): 1. Iden-tification of aerodynamics coefficients of a probe for differ-ent flight conditions given trajectories measurements. Theindustrial objective is to design space vehicles having anaccurate stability. 2. Identification of heat flux coefficientsfrom time domain temperature measurements. The indus-trial objective is the dimensioning of thermal protectionsystem for atmospheric re-entry missions of aerospace vehi-cles. For these two applications, the inverse problem is alsoformulated as a minimization problem with optimal con-trol formulation (lagrangian, adjoint and gradients com-putations and connected to an optimization loop). Firstencouraging results of automatic differentiation procedureon these industrial applications will be presented, with val-idations in agreement with measurements

Stephane alestra, Vassili SrithammavanhEADS INNOVATION [email protected],[email protected]

CP4

Approximating the Solution Set in Multi-CriteriaRadiation Therapy Optimization

Optimal planning of a radiation therapy treatment is amulti-criteria decision problem due to the conflict betweentumor dose and sparing of healthy tissue. An algorithm forgenerating a set of treatment plans such that these consti-tute a representative approximation of the solution set tothis problem is considered. We provide a dual formulationof the algorithm that improves its computational complex-ity, thus extending the range of treatment cases to whichthe algorithm is amenable.

Rasmus BokrantzRoyal Institute of Technology, StockholmRaysearch [email protected]

Anders ForsgrenRoyal Institute of Technology (KTH)Dept. of [email protected]

OP11 Abstracts 75

CP4

Robust Optimization for Proton Therapy Treat-ment Planning

Proton therapy is sensitive to errors such as patient mis-alignments and incorrect treatment volume densities. Fail-ing to account for uncertainties may compromise the treat-ment plan quality drastically. By utilizing informationabout the uncertainties and performing minimax optimiza-tions, we achieve robust treatment plans. We show thatthese plans provide more robustness and better sparingof healthy tissues than those of conventional methods forrobustness, such as using margins and enforcing uniformbeam doses.

Albin FredrikssonRoyal Institute of Technoloy, StockholmRaySearch Laboratories, [email protected]

Anders ForsgrenRoyal Institute of Technology (KTH)Dept. of [email protected]

Bjorn HardemarkRaySearch Laboratories, [email protected]

CP4

A Mathematical Model for Increasing the Effec-tiveness of the Treatment of Cancer Patients

A stochastic model is developed to describe the growth ofheterogenous tumor for dispersed cell regime. The math-ematical model is non-linear stochastic partial differentialequation with a multiplicative colored noise term in thethree dimensional space. The main feature of the modelis that it takes into account random interactions betweentumor cells, immune system cells, and ati-cancer drugs.The existence of weak solutions, pathwise uniqueness andthe convergence in probability of the approzimated solu-tions to the exact solution of the stochastic problem areestablished. Some applications are suggested. The math-ematical results of the study make possible the construc-tion of computer programs and simulations for predictingthe effect of chemotherapy, immunotherapy or genether-apy for each patient. The main idea of this study is: tak-ing into consideration the biomedical parameters of eachpatient and the computer simulations for chemotherapy,immunotherapy or genetherapy, it will support and assistthe medical staff to identify the most effective treatmentsfor each cancer patient.

Fejzi KolaneciUniversity of New York, [email protected]

CP4

Models and Algorithms for Imat and Vmat ArcTherapy Plan Optimization in Radiation Oncology

In contrast with traditional IMRT, an IMAT orVMAT machine delivers radiation in a non-stop fashionwhile the gantry moves continuously during treatment.IMAT/VMAT machines allow the possibility of deliveringhigh-quality treatments in shorter time than IMRT. How-ever, their complex settings require new classes of modelsand algorithms to design treatment plans that take ad-

vantage of this technology. We propose some exact andheuristic approaches, and present results on real patientdata.

Marina A. Epelman, Fei Peng, Edwin RomeijnUniversity of MichiganIndustrial and Operations [email protected], fei peng ¡[email protected]¿,[email protected]

CP4

An Inexact Algorithm in Function Space for Opti-mization with Non-Linear Pdes

We consider an algorithm for non-linear equality con-strained optimization in function space, which is tayloredfor optimization problems with non-linear PDEs. The al-gorithm computes inexact steps in function space, whereinexactness arises from the discretization of a PDE. Dis-cretization errors are controlled by an a-posteriori errorestimation and adaptive grid refinement. As an applica-tion we present a problem from medical therapy planning.

Anton SchielaZIB, [email protected]

Martin WeiserZuse Institute (ZIB)Berlin, [email protected]

CP4

Optimization of Freezing and Thawing Protocolsfor Reduction of Injuring Effects of Cryopreserva-tion

Mathematical models of ice formation inside and outsideof living cells during freezing and thawing are derived byapplying an appropriate averaging technique to partial dif-ferential equations describing the dynamics of water-to-icephase change. This reduces spatially distributed relationsto a few ordinary differential equations with control pa-rameters and uncertainties. Additionally, state constraintsare introduced to avoid the excessive heating of cells. Theobtained equations together with an appropriate objectivefunctional that expresses some injuring effects of cell freez-ing or thawing are considered as a conflict-controlled prob-lem where the aim of the control is to minimize the objec-tive functional, and the aim of the disturbance is opposite.A stable finite-difference scheme for computing the valuefunction of this problem is developed. Using the computedvalue function, optimized cooling and thawing protocolsare designed.

Varvara Turova, Nikolai D. Botkin, Karl-Heinz Hoffmann,Natalie MayerTechnische Universitat Munchen, Department ofMathematicsChair of Mathematical [email protected], [email protected],[email protected], [email protected]

CP5

Selection of Districts for Data Entry Sites in East-

76 OP11 Abstracts

ern Java Household Census

Eastern Java has 38 districts and an estimated popula-tion size of thirty eight millions. District can be kabu-paten or kota such as Kediri, Malang, Pasuruan, if itis a kabupaten then the word kabupaten is not written.Most economical data entry is achieved with six districtsas data entry sites serving Eastern Java , they are 22Bo-jonegoro, 08Kediri, 15Malang, 20Probolinggo, 25kotaSur-abaya, 35Jember . Since 25kota Surabaya has a short dis-tance to provincial capital, 25kota Surabaya can serve asan alternative to data entry in provincial capital. Undercurrent plan, provincial capital is preselected as data entrysite. This work however is done without such constraintas preselected provincial capital . This work is minimiz-ing cost by p-median linear programming. Cost includesscanner price and questionnaire delivery cost.

Rosa DahliaSTISpope [email protected]

CP5

Risk Aversion in The Newsvendor Problem withUncertain Supply: CVaR Criterion

In this presentation, we consider a production firm withstochastic yield. We assume the decision maker is risk-averse and wants to optimize and control the risk of short-fall. The model is one-period and the decision variablesare selling price and the mean of production quantity. Thedecision criterion which is used, is the Conditional Valueat Risk(CVaR).

Saman Eskandarzadeh, Kourosh EshghiSharif University of [email protected], [email protected]

CP5

Dynamic Graph Generation and AsynchronousParallel Bundle Methods for Train TimetablingProblems

The Train Timetabling Problem deals with finding conflictfree routes for different trains in a railway network. A tra-ditional approach uses Lagrangian decomposition of cou-pling constraints in a network flow model. We develop dy-namic graph generation techniques and asynchronous par-allel bundle methods optimizing over dynamically deter-mined subspaces to handle the very large scale instancesfrom the railway-network of Deutsche Bahn.

Frank FischerChemnitz University of [email protected]

Christoph HelmbergTU [email protected]

CP5

Modified Balanced Assignment Problem in VectorCase

We extend the well known balanced assignment problemto the case where costs are expressed by m-dimensionalvectors. For the balanced assignment problem, a polyno-mial time algorithm has been proposed. Our problem is

as follows : find the one to one correspondence betweentwo sets of vectors that minimizes the maximal differenceof the maximum sum and the minumum one. We proposeapproximate algorithms that use the searching method forthe balanced assignment problem.

Yuusaku Kamura, Mario NakamoriTokyo A&T [email protected], [email protected]

CP5

A Distributed Optimization Framework for Maxi-mizing Occupant Comfort in Smart Buildings

We propose a distributed optimization framework for max-imizing the thermal comfort of occupants in a smart build-ing, subject to occupant preferences, HVAC equipment,and energy constraints, by modeling the building as a hi-erarchical, distributed parameter system. We propose dif-ferent algorithms to decompose the resulting non-convex,constrained optimization problem into subproblems, thatare solved by multiple agents. At each timestep, the agentsplay a cooperative game and converge to an equilibrium todecide the optimal values of the building operational vari-ables. Our experimental evaluation shows that the cou-pling among the variables and constraints affects the per-formance of the distributed algorithms and that the opti-mal comfort achieved by the distributed algorithms is com-parable to that of the centralized approach.

Sudha Krishnamurthy, Arvind RaghunathanUnited Technologies Research [email protected], [email protected]

CP5

Scheduling Algorithm for Sensors on Network

We consider a scheduling algorithm for optical spacesurveillance sensors on a network. The algorithm is struc-tured in several stages of approximation using linear pro-gramming formulation in each stage, such as bin-packingor traveling salesman, to closely approximate an optimalsolution. We present results for 1500 satellites over a24h scheduling period. Using only one optical sensor,the results compare very favorably to an analogous greedyscheduling algorithm. We also present results using 3 op-tical sensors.

Zoran SpasojevicMassachusetts Institute of Technology - [email protected]

CP6

Allocation of Maximal Capacities in Gas Networks

Given a gas network, we search an optimal allocation of ca-pacities for each supply and demand node. An allocation isfeasible if each request (supply equals demand) is guaran-teed to be transportable through the network. We proposean algorithm for solving a reduced variant of the capacityallocation problem using an MIP relaxation of the original(nonconvex) MINLP transportation problem as black box.The suitability of our approach is demonstrated on real-lifegas network instances.

Christine HaynUniversity of Erlangen-NurembergEDOM

OP11 Abstracts 77

[email protected]

Lars ScheweFriedrich-Alexander-Universitat Erlangen Nurnberg,Department Mathematik, [email protected]

Alexander MartinUniversity of [email protected]

CP6

Topology Planning for Natural Gas DistributionNetworks

We present a procedure for topology planning of large-scalereal-world natural gas distribution networks. For a givenbudget, it decides which combination of network extensionssuch as additional pipelines, compressors or valves shouldbe added to increase the network’s capacity or enhanceits operational flexibility. We formulate this as a nonlin-ear mixed-integer problem. For its solution we use a com-bination of linear outer approximation and NLP solutiontechniques. Computational results obtained by a specialtailored version of the MINLP solver SCIP are presented.

Armin FugenschuhZuse Institut [email protected]

Thorsten KochZuse Institute [email protected]

Jesco Humpola, Robert Schwarz, Thomas Lehmann,Jonas Schweiger, Benjamin Hiller, Jacint SzaboZuse Insitut [email protected], [email protected], [email protected],[email protected], [email protected], [email protected]

CP6

Mixed-Integer-Programming Methods for GasNetwork Optimization

We present methods to formulate and solve MINLPs origi-nating in stationary gas network optimization. To this aimwe use a hierachy of MIP-relaxations and a graph decom-position approach. Thus, we are able to give tight relax-ations of the underlying MINLP. The methods we presentcan be generalized to other non-linear weakly-coupled net-work optimization problems with binary decisions. We givecomputational results for a number of real world instances.

Lars Schewe, Bjoern GeisslerFriedrich-Alexander-Universitat Erlangen Nurnberg,Department Mathematik, [email protected],[email protected]


Antonio MorsiFriedrich-Alexander-Universitat Erlangen Nurnberg,Department Mathematik, [email protected]

CP6

A MINLP Primal Heuristic for Gas Networks

We consider the problem of stationary optimization in gasnetworks. The combination of nonlinear gas dynamics to-gether with combinatorial aspects of switchable networkdevices leads to very difficult mixed integer nonlinear opti-mization problems. We present a MINLP primal heuristicthat models most of the combinatorial aspects by smoothapproximations or relaxations and additionally incorpo-rates ODEs of gas dynamics and highly detailed modelsof active devices. The practicability of our approach isshown on real-world instances.

Martin SchmidtLeibniz Universitat HannoverInstitute of Applied [email protected]

Marc SteinbachLeibniz Universitat [email protected]

Bernhard WillertInstitute of Applied MathematicsLeibniz Universitat [email protected]

CP6

Technical Capacities of Gas Networks

Announcing the maximal technical capacities of gas net-works is a legal demand against network operators. Exam-ining the gas network with detailed modeling of gas physicsleads to highly nonlinear problems with discrete decisions.Occurring non-convexities and holes in the feasible regionadditionally complicate the computation of the maximaltechnical capacity. With the help of minimal network ex-amples the catch of the problem is explained and its com-plexity is shown.

Martin SchmidtLeibniz Universitat HannoverInstitute of Applied [email protected]


Bernhard WillertInstitute of Applied MathematicsLeibniz Universitat [email protected]

CP6

Designing Multiple Energy Carrier Networks

We consider a network design problem where single energycarrier networks are coupled by cogeneration plants. Mod-eling the physical properties results in a complex mixed-integer nonlinear problem which is approximated by amixed-integer linear model using piecewise linear functions.This mixed-integer program is solved using a branch-and-cut approach which is enhanced by problem-specific mixed-integer programming methods.

Andrea Zelmer, Debora MahlkeFriedrich-Alexander-Universitat Erlangen-Nurnberg

78 OP11 Abstracts

Lehrstuhl fur [email protected],[email protected]


CP7

Finding Low-Rank Submatrices with NuclearNorm and l1-Norm

We propose a convex optimization formulation using nu-clear norm and l1-norm to find a large low-rank submatrixfor a given matrix. We are able to characterize the low-rank and sparsity structure of the resulting solutions. Weshow that our model can recover low-rank submatrices formatrices with subgaussian random noises. We solve theproposed model using a proximal point algorithm and ap-ply it to an application in image feature extraction.

Xuan Vinh DoanC&O DepartmentUniversity of [email protected]

Stephen A. VavasisUniversity of WaterlooDept of Combinatorics & [email protected]


CP7

Convergence Properties for a Self-Dual Regulariza-tion for Convex and Saddle Functions

The convergence properties for a one-parameter regulariza-tion technique for convex optimization problems are stud-ied. Such regularization scheme, introduced by Goebel,has as its main feature its self-duality with respect to theusual convex (and saddle) conjugation. In particular, weshow that if a saddle function has at least one saddle point,then the sequence of saddle points of the regularized saddlefunctions converges to the saddle point of minimal norm ofthe original one.

Alvaro J. GuevaraLouisiana State UniversityDepartment of [email protected]

CP7

Integration of Univariate and Bivariate PiecewiseHigher Order Convex Functions by Bounding

A new numerical integration method is proposed for uni-variate piecewise higher order convex functions. Themethod uses piecewise polynomial lower and upper boundson the function, created in connection with suitable dualfeasible bases in the univariate discrete moment problemand the integral of the function is approximated by tightlower and upper bounds on them. We provide the exten-tion of the method for the bivariate case and numerical

illustrations for some probability density functions.

Mariya NaumovaRutgers University, NJ, [email protected]

Andras PrekopaRutgers [email protected]

CP7

On Rate of Convergence of Discretization Methodsfor Semi-Infinite Minimax Problems

This presentation deals with semi-infinite minimax prob-lems and their solution by discretization algorithms. Thesealgorithms apply an algorithm map to solve approximateproblems obtained by replacing the uncountable numberof functions in the original problem by a finite number offunctions. We develop rate of convergence results for suchalgorithms as a computational budget increases and findthat the asymptotic rate is the same for different algorithmmaps used to solve the approximate problems.

Johannes O. RoysetAsst. Prof.Naval Postgraduate [email protected]

Eng Yau PeeNaval Postgraduate [email protected]

CP7

On Implementing a Homogeneous Interior-PointAlgorithm for Nonsymmetric Conic Optimization

Based on earlier work by Nesterov, an implementation ofa homogeneous interior point algorithm for nonsymmet-ric conic optimization is presented. The method computes(nearly) primal-dual symmetric approximate tangent di-rections followed by a primal centering procedure. Quasi-Newton updating is employed to compute higher order di-rections and to reduce work in the centering process. Ex-tensive and promising computational results are presentedfor facility location problems, entropy problems and ge-ometric programs; all formulated as nonsymmetric conicoptimization problems.

Anders Skajaa, John Bagterp JørgensenTechnical University of [email protected], [email protected]

Per Christian HansenTechnical University of DenmarkInformatics and Mathematical [email protected]

CP8

Adjoint Subgradient-Propagation by AlgorithmicDifferentiation

Optimization problems in engineering often have noncon-vex objective and constraints and require global optimiza-tion algorithms. Deterministic global optimization algo-rithms based on branch-and-bound methods solve relax-ations of the original program. These are constructedby convex/concave under-/over-estimators of the func-

OP11 Abstracts 79

tions involved. One of the alternative methods to con-struct these estimating functions are McCormick relax-ations [McCormick, Computability of global solutions tofactorable nonconvex programs: Part I. Convex underesti-mating problems, Mathematical Programming, 1976]. InGeneral this technique results in nonsmooth estimators.Hence to obtain derivative information, subgradients areneeded. These can be calculated using Algorithmic Dif-ferentiation (AD) techniques as shown in [Mitsos et al,McCormick-Based Relaxations of Algorithms, SIAM Jour-nal on Optimization, 2009] and [Corbett et al, Compiler-Generated Subgradient Code for McCormick Relaxations,ACM Transactions on Mathematical Software, submitted].In this talk we present a method for calculating subgra-dients by an adjoint method which makes the complexityof subgradient computation independent of the number ofoptimization parameters. Thus one bottleneck on the wayto large-scale global optimization is eliminated.

Markus BeckersGerman Research School for Simulation SciencesLuFG Informatik 12: [email protected]

Uwe NaumannRWTH Aachen UniversitySoftware and Tools for Computational [email protected]

Viktor MosenkisLuFG Informatik 12: STCERWTH Aachen [email protected]

Alexander MitsosDepartment of Mechanical EngineeringMassachusetts Institute of [email protected]

CP8

Particle Swarm Optimization in the Analysis of theTwo Process Model of Sleep Regulation

The two process model of sleep regulation is widely usedto understand the sleep-wake cycle in humans. Althoughthe model is typically tuned to produce monophasic sleepwith a duration in the neighborhood of 8 hours, it alsoadmits solutions with a much richer character. By carefulchoice of objective function, a global optimization schemesuch as particle swarm optimization can lead to a numberof different stable sleep-wake scenarios.

Cavendish Q. McKay, David Hickman, Max KenngottMarietta [email protected], [email protected],[email protected]

CP8

Increased Solution Quality for the Tsp with GaRank-Based Selection Method

This study examines the solution quality of some travellingsalesman problem (TSP) instances solved with two geneticalgorithm (GA) selection schemes; proportional roulettewheel and rank-based roulette wheel. By using the samecrossover and mutation operation, the results show thatrank-based selection outperformed proportional selectionin reaching minimum travelling distance within acceptablecomputation time. Results also reveal that proportional

selection becomes susceptible to premature convergence asproblem size increases.

Noraini Mohd [email protected]

CP8

Metamodel-Based Global Optimization Using Dy-namic Radial Basis Function

To enhance the efficiency of modern engineering optimiza-tions involving computational-intensive models, metamod-els become more and more attractive. The main contri-bution of this work is to explore a new dynamic meta-model approach based on radial basis function, which im-proves the approximate accuracy of metamodel in the re-gion which designers are interested in, and makes optimiza-tion converged to the global optimization with minimumevaluations of expensive models. In several testing prob-lems, the efficiency of SRBF is demonstrated.

Lei PengSchool of Areospace EngineeringBeijing Institute of [email protected]

Li Liu, Teng LongSchool of Aerospace EngineeringBeijing Institute of [email protected], [email protected]

CP8

Midaco on Continuous and Mixed Integer SpaceApplications

MIDACO is a novel software for global optimization of con-tinuous, combinatorial and mixed integer problems. Thesoftware is based on a stochastic Gauss approximation al-gorithm (also known as Ant Colony Optimization) that in-corporates the Oracle Penalty Method to handle nonlin-ear equality and inequality constraints. This contributiondiscusses the application of MIDACO on some challeng-ing optimization problems arising from space applications.This is the well known set of continuous GTOP benchmarkproblems published by the ESA/ACT and a mixed inte-ger multi stage optimal control application, representing amulti gravity assist interplanetary space mission. Compar-ing the performance with other approaches on the GTOPbenchmark set, MIDACO obtains very good results andeven reveals new best known solutions in some cases. Incase of the mixed integer interplanetary mission, MIDACOis able to provide a first solution to this kind of complexapplication.

Martin SchlueterSchool of MathematicsUniversity of Birmingham (UK)[email protected]

Matthias GerdtsUniversity of [email protected]

Jan RueckmannUniversity of [email protected]

80 OP11 Abstracts

CP8

Optimal Positioning of Microphones for EngineNoise Measurement

With an ever increasing air traffic,the reduction of noisepollution due to engines is a major issue for aircraft manu-facturers.The prediction of the acoustic sources inside thenacelle is essential to master the acoustic radiation of theengine and design noise reduction solution. Moreover, testfacilities have to be optimized in terms of microphonespositioning and number. An inverse method allowing torebuild acoustic sources from microphones measurementis presented. It is based on a 3D parallel Boundary Ele-ments Method solving the acoustic waves equation in thefrequency domain and using a transfer matrix formulation.The inverse problem is solved by a least square minimiza-tion approach. Finally, a heuristic based on local search ona discretized subspace of possible locations (hill climbing,tabu search) is presented to solve the problem of optimalmicrophones positioning. The purpose is to find the loca-tion and the minimum number of microphones that recon-structs at best an a priori known source.

Vassili Srithammavanh, Regis Lebrun, Stephane alestraEADS INNOVATION [email protected], [email protected],[email protected]

CP9

Milano: A Matlab-Based Toolbox for Minlp

In this talk, we present details of MILANO (Mixed-IntegerLinear and Nonlinear Optimizer), a Matlab-based tool-box for solving mixed-integer optimization problems. ForMINLP, it includes implementations of branch-and-boundand outer approximation algorithms and solves the non-linear subproblems using an interior-point penalty methodintroduced by Benson and Shanno (2005) for warmstarts.Special consideration is given for problems with cone con-straints. Numerical results will be presented.

Hande Y. BensonDrexel UniversityDepartment of Decision [email protected]

CP9

A New (Parallel) Algorithm for Nonlinear Pro-gramming

We propose a new parallel algorithm for solving the gen-eral nonlinear constrained optimization problem on a set ofshared-memory parallel processors. The algorithm is not adirect parallelization of an existing method. The objectivein its design is to achieve an inherently parallel algorithmthat performs comparable to the state-of-the-art methodseven when sequentially applied. The algorithm only re-quires the solution of a sequence of unconstrained prob-lems and linear programs that are interrelated but can besolved concurrently to a degree. We provide numerical ex-amples illustrating the potential of the proposed algorithmand study its convergence behavior.

Figen OztoprakSabanci [email protected]

Ilker S. BirbilSabanci University

[email protected]

CP9

A Hybrid Optimization Algorithm for SolvingTime Dependent Pde-Constrained OptimizationProblems

One approach to solving time dependent PDE problems onparallel machines is to divide the time into intervals and es-timate (by solving the problem on a coarse mesh first) theinitial conditions. One can then iterate to make the solu-tion across the intervals be smooth. We describe a methodthat integrates such an approach with the additional re-quirement to optimize some objective. We illustrate thealgorithm by applying it to the optimal control of a flap-ping wing and using a modified version of the code PITA(Parallel Implicit Time-integration Algorithm).

Walter MurrayDept of Management Science andEngineering, Stanford [email protected]

Youngsoo ChoiStanford [email protected]

CP9

Recent Advances in Solving Milp Problems withSas

We give an overview of SAS software to solve various typesof optimization problems with a focus on mixed integerlinear programming. The talk discusses current researchtopics of the SAS/OR development team including searchstrategies, heuristics and LP integration.

Philipp M. ChristophelSAS Institute [email protected]

CP9

Structure-Exploiting Parallel Solver for Tree-Sparse KKT Systems

By exploiting the rich hierarchical structure in KKT sys-tems of tree-sparse programs recursive algorithms not onlyreduce the solution computation to linear complexity butare also well suited for massive parallelization. A sophis-ticated separation of the underlying tree structure reducescommunication and idle time and leads to an ideal exploita-tion of the multicore system with an almost linear speed-up. The parallel approach and computational results withshared and distributed memory systems will be presented.

Jens HubnerInstitute of Applied MathematicsLeibniz Universitat [email protected]


CP10

Convergence Analysis of a Family of a Family ofDamped Quasi-Newton Methods for Nonlinear Op-

OP11 Abstracts 81

timization

In this talk we will extends the technique in the dampedBFGS method of Powell (Algorithms for nonlinear con-straints that use Lagrange functions, Math. Program-ming, 14: 224–248, 1978), in augmented Lagrange and SQPmethods for constrained ptimization, to a family of quasi-Newton methods with applications to unconstrained opti-mization problems. An appropriate way for defining thisdamped-technique will be suggested to enforce safely thepositive definiteness property for all quasi-Newton positiveand indefinite updates. It will be shown that this techniquemaintains the global and superlinear convergence propertyof a restricted class of quasi-Newton methods for convexfunctions. This property is also enforced on an interval ofnonconvergent quasi-Newton methods. Numerical experi-ences will be described to show that the proposed techniqueimproves the performance of quasi-Newton methods sub-stantially in certain robust cases (eg, the BFGS method)and significantly in inefficient cases (eg, the DFP method).

Mehiddin Al-BaaliSultan Quaboos [email protected]

CP10

On the Solution of the Gps Localization and CircleFitting Problems

We consider the problem of locating a user’s position froma set of noisy pseudoranges to a group of satellites. Two dif-ferent formulations are studied: the nonlinear least squaresformulation in which the objective function is nonconvexand nonsmooth, and the nonlinear squared least squaresvariant in which the objective function is smooth, butstill nonconvex. We show that the squared least squaresproblem can be solved efficiently, despite is nonconvexity.Conditions for attainment of the optimal solutions of bothproblems are derived. The problem is shown to have tightconnections to the well known circle fitting and orthogonalregression problems. Finally, a fixed point method for thenonlinear least squares problems is derived and analyzed.

Amir BeckFaculty of Industrial Engineering and ManagementTECHNION - Israel Institute of [email protected]

Dror PanTechnion - Israel Institute of [email protected]

CP10

A Globaly Convergent Inexact Restoration MethodUsing Lagrange Multipliers

In this work we present a new Inexact Restoration method,combining the basic ideas of the Fischer-Friedlandermethod with the use of Lagrange multipliers, a sharp La-grangian as a merit function, and the use of a quadraticmodel in the optimization fase. We show an example inwhich the original method suffers from the Maratos effectbut not ours. Also a watchdog strategy combining thisnew global method with the Birgin-Martınez local methodis proposed.

Luis Felipe [email protected]

Jose Mario MartınezDepartment of Applied MathematicsState University of [email protected]

CP10

Constrained Optimization Algorithms Using Direc-tions of Negative Curvature

In this work, we show how to include low cost procedures toimprove directions of negative curvature within an interior-point algorithm for constrained optimization, extending re-sults for the unconstrained case. The key feature is thatthe directions are computed within the null subspace ofthe Jacobian matrix of the constraints. Finally, some nu-merical experiments are presented, including real problemsfrom the CUTEr collection, and simulated problems witha controlled spectral structure.

Javier Cano, Javier M. MoguerzaRey Juan Carlos [email protected], [email protected]

Francisco J. PrietoCarlos III [email protected]

CP10

A Sparse Augmented Lagrangian Algorithm forMinimizing the Kohn-Sham Energy

With the constantly increasing power of computers, therealm of experimental chemistry is increasingly beingbrought in contact with the field of computational math-ematics. In particular, the ability to compute the chargedensity, i.e., the probabilistic location of a molecule’s elec-trons, allows numerous properties of matter to be displayedgraphically, as opposed to investigated in the chemistry lab.As many current methods scale at a rate proportional tothe cube of the number of atoms, such problems are stilltoo large for direct ab initio computations. This work de-scribes recent advances in using an augmented Lagrangianapproach to minimizing a specific energy function underorthogonality-constraints. Scaling is obtained by relaxingfull-orthogonality and exploiting the local properties of themolecular systems in question.

Marc MillstoneCourant Institute of Mathematical SciencesNew York [email protected]

Chao YangLawrence Berkeley National [email protected]

Michael L. OvertonNew York UniversityCourant Instit. of Math. [email protected]

Juan C. MezaLawrence Berkeley National [email protected]

CP10

Can Directional Hessian Refinement Reduces

82 OP11 Abstracts

Quasi-Newton Iterations by More Than Half?

Directional Hessian refinement was recently proposed forBFGS quasi-Newton method with BFGS as the refiner, ap-proximately halving iteration numbers but doubling cost ineach iteration. Here we report experiments in which DFP isused as the refiner for the DFP quasi-Newton method. Ex-perimental data showed that the DFP refiner consistentlyreduces iteration numbers substantially for problems forwhich the DFP method converges slowly, and in one caseit reduced iterations from 3975 to 73.

Yu ZhuangTexas Tech [email protected]

CP11

Lll-Based Polynomial Time Algorithm for IntegerKnapsacks

In this talk we will discuss a recent application of lattice ba-sis reduction to the computational integer knapsack prob-lem. We obtain a LLL-based polynomial time algorithmthat solves the problem subject to a geometric constraint.

Iskander AlievCardiff [email protected]

CP11

Cutting Planes for Mixed Integer Programs withQuadratic Constraints and Objectives

We discuss some heuristics to generate cutting planes formixed-integer programs which have quadratic constraintsor a quadratic objective, and present computational resultson a a number of instances, including some from Mittel-mann’s library of instances.

Sanjeeb DashIBM T.J. Watson Research [email protected]

Marcos GoycooleaUniversidad Adolfo Ibanez, [email protected]

CP11

A Polynomial-time Algorithm for Separable Con-vex Minimization over N-fold 4-block Decompos-able IPs

In this talk, we generalize N-fold IPs and two-stagestochastics IPs with N scenarios to N-fold 4-block decom-posable integer programs. We show that for fixed blocksbut variable N , these integer programs are polynomial-timesolvable for any separable convex function that is to beminimized. This implies, for example, that for given fixednetwork, stochastic integer multi-commodity flow problemscan be solved in polynomial time in the number of scenar-ios and commodities and in the binary encoding length ofthe input data.

Raymond HemmeckeDept. of MathematicsTechnische Univ. Munchen [email protected]

Matthias KoppeDept. of MathematicsUniversity of California, Davis, [email protected]

Robert WeismantelETH [email protected]

CP11

Irreducible Infeasible Sets in Convex Integer Pro-grams

In this paper we address the problem of the infeasibility ofsystems defined by convex inequality constraints, wheresome or all of the variables are integer. In particular,we provide an algorithm that identifies a set of all con-straints that may affect a feasibility status of the systemafter some perturbation of the right-hand sides. Further-more, we analyse properties of the irreducible infeasiblesets and we investigate the problem of the maximal con-sistent partition, showing that for the considered class ofconvex functions the system can be partitioned into twosubsystems each of which has an integer solution.

Wieslawa T. ObuchowskaDepartment of MathematicsChowan [email protected]

CP11

Designing An Efficient Branch-and-Bound Ap-proach for Exact Mixed-Integer Programming

We present a hybrid symbolic-numeric approach for solvingmixed-integer-programming problems exactly over the ra-tional numbers. By performing many operations using fastfloating-point arithmetic and then verifying and correctingresults using symbolic computation, exact solutions canbe found without relying entirely on rational arithmetic.Computational results will be presented based on an ex-act branch-and-bound algorithm implemented within theconstraint integer programming framework SCIP.

Daniel [email protected]

William CookGeorgia Institute of [email protected]

Thorsten Koch, Kati WolterZuse Institute [email protected], [email protected]

CP12

An Optimal Control of Probability Density Func-tions of Stochastic Processes with the Fokker-Planck Formulation

An optimal control strategy of stochastic processes is for-mulated by using the Fokker-Planck model. The controlobjectives are defined based on the probability densityfunctions and the optimal control is achieved as the min-imizer of the objective under the constraint given by theFokker-Planck equation. The purpose of the control is at-taining a final target configuration, or tracking a desired

OP11 Abstracts 83

trajectory, for which a receding-horizon algorithm over asequence of time windows is implemented.

Mario AnnunziatoUniversita degli Studi di SalernoDipartimento di Matematica e [email protected]

CP12

Optimal Flow Control Based on POD for the Can-cellation of Tollmien-Schlichting Waves by PlasmaActuators

We present a Model Predictive Control approach for thecancellation of Tollmien-Schlichting waves in the bound-ary layer. To control the flow a bodyforce is inducedby a plasma actuator. Proper Orthogonal Decompositionis used for the low-order description of the flow model.We show methods for improving the reduced model whosequality is verified in comparison to the results of a FiniteVolume based Large Eddy simulation. Numerical resultsof the cancellation will be presented.

Jane ElsemullerTechnische Universitat DarmstadtGraduate School of Computational [email protected]


CP12

Crank-Nicolson and Stormer-Verlet Discretiza-tion Schemes for Optimal Control Problems withParabolic Partial Differential Equations

In this talk we present a family of second order discretiza-tion schemes for parabolic optimal control problems basedon Crank-Nicolson schemes with different time discretiza-tions for state and adjoint state so that discretization andoptimization commute. One of the schemes can be ex-plained as the Stormer-Verlet scheme. So we can interpretthe method in the context of geometric numerical integra-tion. The Hamiltonian structure of parabolic optimal con-trol problem is also discussed.

Thomas FlaigUniversitat der Bundeswehr MunchenInstitut fur Mathematik und [email protected]

Thomas ApelUniversitat der Bundeswehr [email protected]

CP12

Multilevel Optimization for Flow Control with Dis-crete Adjoints

We present a technique to efficiently obtain the discrete ad-joint via a sparsity-exploiting forward mode of AutomaticDifferentiation. This approach has been applied to a fastCFD code including turbulence models. Using the adjoint,we can apply multilevel optimization techniques. Theseare well suited for flow control problems, since we have dif-ferent discretization levels and models of increasing com-

plexity (POD, RANS, LES). Numerical results includingunsteady problems and shape optimization will be given.

Rolf RothTU [email protected]


CP12

Optimal Control of a Melt Flow in Laser Cutting

We consider optimal control for a mathematical model of amelt flow in laser cutting. The optimization goal is to find alaser intensity function that keeps the two free boundariesof the flow region as close as possible to the stationarysolution. The dynamical behavior of the free boundariesis described by a system of two nonlinear coupled partialdifferential equations. We discuss theoretical aspects andpropose a numerical solution.

Georg Vossen

Nonlinear Dynamics of Laser Processing (NLD)RWTH Aachen [email protected]

CP13

Shortest Path Estimation of Mra Images Using Ge-netic Algorithm

MRA, a technique used to detect vascular pathologies dur-ing brain surgery, provides 3D data of cerebral vascularstructures. Where it is difficult to access the region ofinterest, the best point of entry is found. Choosing theshortest path with the minimum inconvenience is a rout-ing problem. We discuss the use of Genetic Algorithm toestimate the shortest path between two points in the sys-tem of blood vessels in the brain using skeletonized MRAimages.

Anthony Y. AidooEastern Connecticut State [email protected]

Joseph Ackora-PrahKwame Nkrumah University of Science and TechnolygyKumasi, [email protected]

CP13

Influenza Vaccination Strategies When Supply IsLimited

The aim of this work is to find alternatives that mitigatethe transmission of influenza via limited vaccination in afinite (200 days) time period. To understand the dynamicsof transmission we will use an extension of the SIR modelwith data from the 1918-19 Pandemic Influenza. We useoptimal control techniques to explore these constraints andprovide a more realistic approach that public health Policymakers can work with when facing a Pandemic threat.

Romarie MoralesArizona State [email protected]

84 OP11 Abstracts

Sunmi LeeMathematical, Computational and Modeling SciencesCenter,Arizona State University,[email protected]

Carlos Castillo-ChavezArizona State University andDepartment of [email protected]

CP13

A Multiple Sequence Alignment Algorithm basedon Compression

Multiple alignments play an important role in detectingconserved subregions among biological sequences and infer-ring evolutionary history. Many alignment methods thatexist to date do not use the specific properties of biologicalsequences and suffer from bad quality or high computa-tional cost. Here, we introduce an approach that is basedon compression and combinatorial optimization techniques.It uses common subsequences to produce alignments andtherefore runs faster on sets of sequences that share com-mon properties.

Susanne PapeFAU Uni-Erlangen, GermanyChair of [email protected]

Sebastian PokuttaMassachusetts Institute of [email protected]


CP13

Parameters Optimization in S-System Models us-ing Population-based Reverse Engineering Meth-ods

Reverse Engineering can be considered as a process fromwhich is possible inferring structural and dynamics featuresof a given system from external observations and relevantknowledge. RE techniques play a central role in systemsbiology, since it is not only important a knowledge of genesand proteins, but also to understand their structures anddynamics. RE works for inferring genetic networks arebased on evolutionary algorithms, because they are appli-cable where mathematical analysis fail.

Mario PavoneDept. of Maths and C.S. - University of [email protected]

CP14

A Multistage Stochastic Optimization Model forLivestock Production

In this work the authors presents a stochastic optimizationmodel for planning piglet production as a decision supporttool in the first stage of the pig supply chain. The modelincludes the uncertainty in the sow biological behaviour aswell as in future prices, under a finite set of possible scenar-ios. The proposed model provides an optimal replacement

policy and schedules purchases of gilts during a mediumterm planning horizon, based on weekly periods. In ouropinion, the stochastic programming framework providesa flexible and effective decision support tool for planningproduction of swine farm.

Victor M. AlbornozUniv Tech Fed Santa MariaDepartamento de [email protected]

Lluis M. PlaDepartamento de Matematica.Universidad de [email protected]

SARA V. Rodrıguez-SanchezFacultad de Ingeniera Mecanica y ElectricaUniversidad Autonoma de Nuevo [email protected]

CP14

Optimization of Environmental Adaptation Poli-cies

Economic-environmental model with vintage capital is con-structed to analyze the optimal balance among differentcategories of investments into the environmental adapta-tion that compensate negative consequences of environ-mental hazards and changes. The model distinguishesthree categories of adaptation measures that compensatethe decrease of the environmental amenity value, compen-sate the decrease of total productivity, and develop newhazard-protected capital and technology. The results pro-vide insight into rational environmental adaptation poli-cies.

Natali HritonenkoPrairie View A&M [email protected]

Yuri YatsenkoHouston Baptist [email protected]

CP14

Hydrocarbon Reservoir Production Optimizationunder Uncertainty - A Case Example

Sequential Bayesian inversion methods are entering the do-main of updating the knowledge one has about physicalproperties of a reservoir from production measurements.One example of these methods is the ensemble Kalman fil-ter. The result of such methods is an ensemble of modelsrepresenting the posterior uncertainty. The task is to ap-ply production optimization methods to the ensemble. Wepresent an evolutionary algorithm-based approach to thatproblem and apply it to a fairly large benchmark case.

Oliver PajonkInstitute of Scientific ComputingTechnische Universitat [email protected]

Ralf Schulze-RiegertSPT Group [email protected]

OP11 Abstracts 85

Hermann G. MatthiesInstitute of Scientific ComputingTechnische Universitat [email protected]

CP14

Communication Complexity of Scheduling Prob-lems

Motivated by an application from aviation, the optimalutilization of runways, we study the communication com-plexity of scheduling problems. In aviation, there exist anarrival and a departure planning tool which have to com-municate to obtain an optimal schedule.Considering feasibility problems, we investigate communi-cation protocols for scheduling problems. Therefore, weanalyze monochromatic rectangles in symmetric schedul-ing matrices. Furthermore, their relation to protocols andproofs of lower bounds are presented.

Andrea PeterUniversity [email protected]



CP14

Piecewise Monotonic Regression Algorithm forProblems Comprising Seasonal and MonotonicTrends

In this research piecewise monotonic models for problemscomprising seasonal cycles and monotonic trends are con-sidered. In contrast to the conventional piecewise mono-tonic regression algorithms, our approach can efficientlyexploit a priori information about temporal patterns. Itis based on reducing these problems to monotonic regres-sion problems defined on partially ordered data sets. Thelatter are large-scale convex quadratic programming prob-lems. They are efficiently solved by the GPAV algorithm.

Amirhossein SadoghiDepartment of Computer ScienceLinkoping [email protected]

Oleg BurdakovLinkoping [email protected]

Anders GrimvallDepartment of Computer ScienceLinkoping University,[email protected]

CP14

Smaller Compact Formulation for Lot-Sizing withConstant Batches

We consider a variant of the classical lot-sizing problem inwhich the capacity in each period is an integer multiple ofsome basic batch size. Pochet and Wolsey (Math. Oper.

Res. 18, 1993) presented an O(n2 min{n, C}) algorithmto solve this problem and a linear program with MO(n3)variables and inequalities, where n is the number of periodsand C the batch size. We provide a linear program of sizeO(n2 min{n, C}), that is, for C < n, our formulation issmaller.

Ruediger StephanTechnische Universitat [email protected]

CP15

Survivable Network Design Using 3 and 4-PartitionFacets

Given a graph G and a set of traffic demand among nodesof G, the problem is to find minimum cost capacity in-stallation on the edges of G, which will permit a feasiblerouting of all traffic under any single edge failure. We de-rive several families of facets based on 3- and 4-partitionsof G to derive very tight lower bounds, and report optimalsolutions on problems of up to 35 nodes and 70 edges.

Yogesh K. AgarwalIndian Institute of Management, Lucknow, [email protected]

CP15

Local Search for Hop-Constrained Directed SteinerTree Problem with Application to UAV-BasedMulti-Target Surveillance

Given a weighted directed graph with a selected root nodeand a set of terminal nodes, the directed Steiner tree prob-lem (DSTP) is to find a directed tree of the minimal weightwhich is rooted in the root node and spanning all termi-nal nodes. We consider the DSTP with a constraint onthe total number of arcs (hops) in the tree. This prob-lem is known to be NP-hard, and therefore, only heuristicscan be applied in the case of its large-scale instances. Forthe hop-constrained DSTP, we propose local search strate-gies aimed at improving any heuristically produced initialSteiner tree. They are based on solving a sequence of hop-constrained shortest path problems for which we have re-cently developed efficient label correcting algorithms. Theapproach presented in this talk is applied to solving theproblem of 3D placing unmanned aerial vehicles (UAVs)used for multi-target surveillance. The efficiency of our al-gorithms is illustrated by results of numerical experiments.


Patrick DohertyDept. of Computer and Information ScienceLinkoping [email protected]

Kaj HolmbergDepartment of MathematicsLinkoping [email protected]

Jonas Kvarnstrom, Per-Magnus OlssonDept. of Computer and Information ScienceLinkoping [email protected], [email protected]

86 OP11 Abstracts

CP15

Graph Products for Faster Separation of Wheel In-equalities

A stable set in a graph G is a set of pairwise nonadjacentvertices. The problem of finding a maximum weight sta-ble set is one of the most basic NP-hard problems. Animportant approach to this problem is to formulate it asthe problem of optimizing a linear function over the convexhull STAB(G) of incidence vectors of stable sets. Then onehas to solve separation problems over it. Cheng and Cun-ningham (1997) introduced the wheel inequalities and pre-sented an algorithm for their separation using time O(n4)for a graph with n vertices and m edges. We present a newseparation algorithm running in O(mn2 + n3 log n).

Sven De VriesUniversitat [email protected]

CP15

Optimization Methods for Radio Resource Man-agement

We consider heuristic methods for wireless telecommunica-tions cellular systems in which each base station managesthe orthogonal radio resources for its own users. Inter-cellinterference is an issue if nearby cells simultaneously usethe same resource. We discuss the fairness issue for users inthe system. We have previously shown that our optimiza-tion problem is NP-hard and even inapproximable, unlessP is equal to NP.

Mikael P. Fallgren

Royal Institute of Technology (KTH)Optimization and Systems [email protected]

CP15

A Continuous Quadratic Programming Formula-tion of the Vertex Separator Problem

A vertex separator of a connected graph G is a subset ofvertices A whose removal splits G into two disconnectedsubsets B and C. The Vertex Separator Problem is theproblem of finding the smallest such subset A when B andC are subject to size constraints. We formulate the VSPas a continuous quadratic program and provide necessaryand sufficient conditions for local optimality which dependonly on the edges in the graph.

James T. HungerfordUniversity of FloridaDepartment of [email protected]

William HagerUniversity of [email protected]

CP15

Algorithms for Computing a Hamiltonian Cycle byMinimizing a Smooth Function

The holy grail of solving hard binary optimization prob-lems is to find a smooth function whose minimizer are allbinary. We discuss algorithms based on a result that showsminimizing a determinant of a matrix whose variables are

the elements of the adjacency matrix of graph is such afunction whose global minimizer is a Hamiltonian cycle.Finding the global minimizer is not without issues most ofwhich are caused by symmetry induced from the existenceof multiple Hamiltonian cycles. We show that the use ofdirections of negative curvature is instrumental is breakingthis symmetry.

Walter MurrayDept of Management Science andEngineering, Stanford [email protected]

Jerzy FilarCIAMUniversity of South [email protected]

Michael HaythorpeUniversity of South [email protected]

CP16

First-Order Methods for Convex Optimizationwith Inexact Oracle

We introduce a new definition of inexact oracle for con-vex optimization problems, and study the first-order meth-ods (classical and fast gradients) based on this oracle. Welink oracle accuracy and achievable solution accuracy, andshow that only fast gradient suffers from error accumu-lation, casting a doubt over its absolute superiority overthe classical gradient. We present applications to saddle-point problems and obtain a universal optimal method forsmooth and non-smooth convex problems.

Olivier DevolderCenter for Operations Research and EconometricsUniversite catholique de [email protected]

Francois GlineurCenter for Operations Research and EconometricsUniversit’e catholique de [email protected]

Yurii NesterovCOREUniversite catholique de [email protected]

CP16

Bandgap Optimization of Photonic Crystals ViaSemidefinite Programming and Subspace Methods

The mathematical formulation of bandgap optimizationproblems is made tractable by discretizing and using the fi-nite element method, yielding a series of finite-dimensionaleigenvalue optimization problems that are large-scale andnon-convex, with low regularity and non-differentiable ob-jective. By restricting to appropriate eigen-subspaces,we reduce the problem to a sequence of small-scale con-vex semidefinite programs (SDPs) for which modern SDPsolvers can be efficiently applied. Among several illustra-tions we show that it is possible to achieve optimized pho-tonic crystals which exhibit multiple absolute bandgaps,whose structures show complicated patterns which are far

OP11 Abstracts 87

different from existing photonic crystals.

Robert M. FreundMITSloan School of [email protected]

H. MenNational University of [email protected]

JOEL [email protected]

Cuong Nguyen, Pablo A. Parrilo, Jaime PeraireMassachusetts Institute of [email protected], [email protected], [email protected]

CP16

An Optimal Algorithm for Minimizing ConvexFunctions on Simple Sets

We describe an algorithm based on Nesterov’s and onAuslender and Teboulle’s ideas for minimizing a convexLipschitz continuously differentiable function on a simpleconvex set (a set into which it is easy to project a vec-tor). The algorithm does not depend on the knowledge ofany Lipschitz constant, and it achieves a precision ε for theobjective function in O(1/

√ε) iterations. We describe the

algorithm and the main complexity result.

Clovis C. GonzagaFederal Univ of Sta [email protected]

Elizabeth W. KarasFederal Univ. of Parana, BrazilDep. of [email protected]

Diane RossettoUniversity of Sao Paulo, [email protected]

CP16

Subgradient Methods for Convex Problem Basedon Gradient Sampling

We present a new subgradient algorithm, based on gradientsampling, to solve a nondifferentiable constrained convexoptimization problem. Our motivation comes from the factthat the gradient is cheap to compute compared with thesubgradient in many applications. We prove the conver-gence of our proposed algorithm for the primal problem.We also apply our algorithm to the Lagrangian dual ofa convex constrained optimization problem. Numerical re-sults demonstrate that our algorithms are comparable withsome existing subgradient algorithms.

Yaohua HuThe Hong Kong Polytechnic [email protected]

Chee Khian SimDepartment of Applied MathematicsThe Hong Kong Polytechnic University

[email protected]

Xiaoqi YangThe Hong Kong Polytechnic [email protected]

CP16

Implementation and Tests of An Optimal Algo-rithm for Minimizing Convex Functions on SimpleSets

We summarize an algorithm described by the authors forminimizing continuously differentiable functions on simplesets, and incorporate to it adaptive procedures for usingstrong convexity constants. Then we show computationalresults comparing our method to optimal algorithms byNesterov and by Auslender and Teboulle, and to other ef-ficient methods for optimization on simple sets.

Elizabeth W. KarasFederal Univ. of Parana, BrazilDep. of [email protected]

Clovis C. GonzagaFederal Univ of Sta [email protected]

Diane RossettoUniversity of Sao Paulo, [email protected]

CP16

Conjugate Gradient with Subspace Optimization

In this talk, we present Conjugate Gradient with SubspaceOptimization (CGSO), an algorithm for solving uncon-strained optimization problems. CGSO is closely relatedto Nonlinear Conjugate Gradient and Nemirovsky-Yudin’salgorithm from early 80’s, with advantages from each. Wewill address issues on implementation of the algorithm aswell as its properties and convergence rate. In addition toits efficiency in practice, CGSO has a convergence rate ofO(log 1

ε) for the class of strictly convex problems.

Sahar KarimiUniversity of [email protected]


CP17

GloptLab - A Configurable Framework for GlobalOptimization and Introducing the Test Environ-ment

GloptLab is an easy-to-use testing and development plat-form for solving quadratic optimization problems by usingbranch and prune and filtering. In order to avoid a lossof feasible points, rigorous error estimation using intervalarithmetic and directed rounding are used. Various newand state-of-the-art algorithms implemented in GloptLabare used to reduce the search space: constraint propaga-tion, linear relaxations, strictly convex enclosures, conicmethods, probing and branch and bound. Other tech-

88 OP11 Abstracts

niques, such as finding and verifying feasible points, enableto find the global minimum of the objective function. TheTest Environment is a free interface to efficiently test differ-ent optimization solvers. It is designed as a tool for bothdevelopers of solver software and practitioners who justlook for the best solver for their specific problem class. Itenables users to choose and compare diverse solver rou-tines, organize and solve large test problem sets, selectinteractively subsets of test problem sets, perform a sta-tistical analysis of the results and automatically produce aLaTeX and PDF output.

Ferenc DomesFaculty of Mathematics, University of Vienna,[email protected]

Arnold NeumaierUniversity of ViennaDepartment of [email protected]

Martin FuchsCERFACSParallel Algorithms [email protected]

Hermann SchichlUniversity of ViennaFaculty of [email protected]

CP17

A Multi-Step Interior Point Warm-Start Approachfor Stochastic Programming

We present an Interior Point based multi-step solution ap-proach for stochastic programming problems, given by asequence of scenario trees of increasing sizes. These treescan be seen as successively more accurate discretization ofan underlying continuous probability distribution. Eachproblems in the sequence is warmstarted from the previ-ous one. We analyse the resulting algorithm, argue that ityields improved complexity over either the coldstart or anaive two-step scheme, and give numerical results.

Andreas GrotheySchool of MathematicsUniversity of [email protected]

Marco ColomboUniversity of Edinburghm.colombo@ed,ac,uk

CP17

A Bound Constrained Interval Global Optimiza-tion Solver in the COCONUT Environment

In this presentation we introduce coco gop ex, a generalpurpose interval branch–and–bound solver for bound con-strained global optimization. It is written as a solver com-ponent of the COCONUT Environment, a modular open-source software environment for global optimization. Af-ter running coco gop ex on over 150 standard bound con-strained test problems, we concluded that is is competitivewith current state–of–the–art GO solvers such as BARONand outperforms them in many cases.

Mihaly Csaba Markot

Faculty of MathematicsUniversity of [email protected]


CP17

Surrogate Model Choice and Averaging Based onDempster-Shafer Theory for Global OptimizationProblems

The literature on solving global optimization problems us-ing surrogate models shows that the surrogate model choicemay greatly influence the solution quality. However, modeluncertainty has thus far rarely been taken into accountwhen deciding for a specific model. This talk therefore fo-cuses on Dempster-Shafer theory for combining and select-ing surrogate models during the optimization process. Ad-vantages and disadvantages of this approach will be demon-strated on numerical experiments. This is a collaborativework between Tampere University of Technology and Cor-nell University.

Juliane MuellerTampere University of TechnologyVisiting Researcher at Cornell [email protected]

Christine A. ShoemakerCornell [email protected]

Robert PicheTampere University of [email protected]

CP17

Exclusion Regions for Global Optimization Prob-lems

Interval methods for GO often have the difficulty that sub-boxes containing no solution cannot be easily eliminatedif there is a nearby optimizer outside the box. Thus, neareach solution, many small boxes are created by repeatedsplitting. We discuss how to reduce this so-called clus-ter effect by defining exclusion regions around each opti-mizer found, that are guaranteed to contain no other solu-tion. The proposed methods are implemented in the CO-CONUT Environment for global optimization.


Mihaly Csaba MarkotFaculty of MathematicsUniversity of [email protected]

CP17

An Optimal Design of Ball Bearings Using Evolu-tionary Algorithms

In the optimum design of ball bearings the long life is one

OP11 Abstracts 89

of the most important criterions. For solving constrainednon-linear optimization formulations, an optimal designmethodology has been proposed by two evolutionary algo-rithms, namely the artificial bee colony and genetic algo-rithms. A sensitivity analysis of various design parameters,using the Monte Carlo simulation method, has been per-formed to see changes in the dynamic capacity. There is anexcellent improvement found in optimized bearing designs.

Rajiv TiwariProfessor, Department of Mechanical EngineeringIIT [email protected]

U. VenkatesuGraduate Student, IIT [email protected]

CP18

Solving Highly Symmetric Integer Linear Pro-grams

We present a new algorithm which solves integer linearprograms of dimension n with symmetry groups isomorphicto the alternating or the symmetric group of order n. Themain idea of the algorithm is to reduce the problem to afeasibility check of a linear number of certain points lyingclose to the fixed space of the symmetry group. This isjoint work with Richard Bodi and Michael Joswig.

Katrin HerrTU [email protected]

CP18

A Bound for the Number of Different Basic Solu-tions Generated by the Simplex Method

In this presentation, we give an upper bound for the num-ber of different basic feasible solutions generated by thesimplex method for linear programming problems havingoptimal solutions. The bound is polynomial of the num-ber of constraints, the number of variables, and the ratiobetween the minimum and the maximum values of all thepositive elements of primal basic feasible solutions. Whenthe primal problem is nondegenerate, it becomes a boundfor the number of iterations. We show some basic resultswhen it is applied to special linear programming problems.The results include strongly polynomiality of the simplexmethod for Markov Decision Problem by Ye and utilize itsanalysis.

Tomonari Kitahara, Shinji MizunoTokyo Institute of [email protected], [email protected]

CP18

Infeasible Constraint-Reduced Interior-Point forLinear Optimization

Constraint reduction in the context of interior-point meth-ods can yield substantial computational savings per itera-tion for linear programs with many more inequality con-straints than variables in standard dual form. Previouslyproposed constraint-reduced algorithms require initial dualfeasibility. Here an exact-penalty-based framework for in-feasible constraint-reduced primal-dual interior-point algo-

rithms, including a scheme for iterative adjustment of thepenalty parameter, is proposed and analyzed. Promisingnumerical results with an MPC variant (which fits withinthe framework) are reported.

Andre L. TitsUniversity of Maryland, College ParkDept of ECE and Institute for Systems [email protected]

Meiyun Y. HeUniversity of Maryland, College [email protected]

CP18

The Accuracy of Interior-Point Methods Based onKernel Functions

Interior-point methods that use barrier functions inducedby some real univariate kernel functions have been studiedfor the last decade. In these IPM’s the algorithm stopswhen finds a solution such that is close enough (in the bar-rier function sense) to a point in the central path such thatsatisfies some accuracy conditions. But this does not di-rectly imply that we got a solution that has the desiredaccuracy. In this talk, we analyze the accuracy of the so-lution produced by the mentioned algorithm.

Manuel VieiraDelft University of [email protected]

CP18

Strange Behaviors of Interior-Point Methods forSolving Semidefinite Programming Problems inPolynomial Optimization

We observe that in a simple one-dimensional polyno-mial optimization problem (POP), the ’optimal’ values ofsemidefinite programming (SDP) relaxation problems re-ported by the standard SDP solvers converge to the op-timal value of the POP, while the true optimal values ofSDP relaxation problems are strictly and significantly lessthan that value. Some pieces of circumstantial evidencesfor the strange behaviours of the SDP solvers are given.This result gives a warning to users of the SDP relaxationmethod for POPs to be careful in believing the results ofthe SDP solvers. We also demonstrate how SDPA-GMP,a multiple precision SDP solver developed by one of theauthors, can deal with this situation correctly.

Hayato WakiThe University of [email protected]

Maho [email protected]

Masakazu MuramatsuUniversity of [email protected]

CP18

Symmetry in the Basis Partition of the Space ofLinear Programs

A linear program (LP) is associated with an optimal basis.

90 OP11 Abstracts

The space of linear programs (SLP) can be partitioned intoa finite number of sets, each consisting of all LPs with acommon basis. If the partition of SLP can be character-ized, we can solve infinitely many LPs in closed form. Atool for characterizing the partition of SLP is a dynamicalsystem on the Grassmann manifold M’=h(M), where M isa projection matrix. An LP defines a projection matrix,starting from which the solution of M’=h(M) converges toa limit projection matrix which can determine the basis ofthe LP. Some properties on structures of the partition, inparticular, symmetric structures, will be presented.

Gongyun ZhaoDepartment of MathematicsNational University of [email protected]

CP19

Flash Crash, Market Impact, and Stability of Op-timal Execution Strategy

The U.S. market Flash Crash on May 6, 2010 illustratedeffect of trading impact and challenges in optimal execu-tion. In this talk, I will describe market price and impactmodels which have been proposed for developing optimalexecution algorithms. In addition, I will present propertiesof the resulting execution algorithms, describe sensitivity ofexecution strategies to market impact functions, and howto achieve better stability using robust optimization andregularized robust optimization. *This is joint work withT. F. Coleman and S. Moazeni

Yuying LiSchool of Computer ScienceUniversity of [email protected]

CP19

Optimization with Time-Periodic PDE Con-straints: Numerical Methods and Applications

Optimization problems with time-periodic parabolic PDEconstraints can arise in important chemical engineeringapplications, e.g., in periodic adsorption processes. Wepresent a novel direct numerical method for this problemclass. The main numerical challenges are the high non-linearity and high dimensionality of the discretized prob-lem. The method is based on Direct Multiple Shootingand inexact Sequential Quadratic Programming with glob-alization of convergence based on natural level functions.We highlight the use of a generalized Richardson iterationwith a novel two-grid Newton-Picard preconditioner for thesolution of the quadratic subproblems. At the end of thetalk we explain the principle of Simulated Moving Bed pro-cesses and conclude with numerical results for optimizationof such a process.

Andreas PotschkaInterdisciplinary Center for Scientific ComputingUniversity of [email protected]


Johannes SchloderInterdisciplinary Center for Scientific ComputingUniversity of Heidelberg

[email protected]

CP19

A Class of Preconditioners for Newton-KrylovMethods in Large Scale Optimization

In this work, we propose a class of preconditioners forNewton-Krylov methods in nonconvex large scale uncon-strained optimization. We focus on the solution of thelarge scale (possibly indefinite) linear system which arisesat each iteration of any truncated Newton method. In par-ticular, we use the set of directions generated by Krylovsubspace methods, as by product, to provide the precondi-tioners.

Massimo RomaDipartimento di Informatica e SistemisticaSAPIENZA - Universita’ di [email protected]

Giovanni FasanoDip. Matematica ApplicataUniversita’ Ca’ Foscari di [email protected]

CP19

On Saddle Points in Nonconvex Semi-Infinite Pro-gramming

We apply two convexification procedures to the Lagrangianof a nonconvex semi-infinite programming problem. Underthe reduction approach it is shown that, locally around alocal minimizer, this problem can be transformed equiv-alently in such a way that the transformed Lagrangianfulfills saddle point optimality conditions. These resultsallow that local duality theory and corresponding numeri-cal methods (e.g. dual search) can be applied to a broaderclass of nonconvex problems.

Jan-J RuckmannUniversity of [email protected]

Francisco Guerra VazquezUniversity of the [email protected]

Ralf WernerHochschule [email protected]

CP19

Necessary Optimality Conditions for the O-D Ma-trix Adjustment Problem

Most of the work on this topic has been based on assumingthat the traffic assignment problem admits a unique opti-mal flow in a certain neighborhood, which is very strong.Hence, designing necessary optimality conditions for theproblem appears to be crucial, since it is typically nons-mooth. Only Fritz-John’s type necessary optimality con-ditions have been derived so far. In this talk, we presentsome approaches to obtain Karush-Kuhn-Tucker type op-timality conditions using mathematical tools from varia-tional analysis.

Alain B. Zemkoho, Stephan DempeInstiut of Numerical Mathematics and Optimization

OP11 Abstracts 91

TU Bergakademie [email protected], [email protected]

CP20

Simulation of Interface Evolution for SeveralPhases Using a Primal-Dual Active Set Method

Interface evolution with applications including material sci-ence (e.g. grain growth), image processing and geology canbe modelled using a phase field approach. In particular,we consider an Allen-Cahn variational inequality and in-clude nonlocal constraints to guarantee mass conservation.Moreover, due to the consideration of several phases, westudy a system of inequalities. Simulation in time leads toa sequence of optimization problems, where the unknownsare vector valued functions in space, which have to ly in theGibbs-Simplex and additionally have to fulfill an integralcondition. We propose and analyze a primal-dual activeset method for the solution. Convergence of the algorithmis shown and numerical simulations in two and three di-mensions as well as for two and more phases are presenteddemonstrating its efficiency.

Luise BlankNWF I - MathematikUniversitat [email protected]

CP20

Wind Climatologies from a Mass-Consistent WindModel for Small Terrain

Wind measurements in Sri Lanka are sparse particularlyin the hill country of Sri Lanka and interpolation of theseobservations provides unrealistic wind patterns in moun-tainous areas. Here we use a mass-consistent wind modelthat takes account of topography to compute monthly windclimatologies for Sri Lanka at a resolution of 6 km. Themodel predicts realistic wind fields and brings out the highwind speed at various gaps in the mountain ridges in SriLanka. Quantitative comparison with measurements atstations across Sri Lanka shows that the predictions arereasonably realistic. Thus this technique provides detailedand useful wind climatologies that can be used for research,development and applications purposes.

Ajith GunaratneFlorida A & M UniversityDepartment of [email protected]

CP20

Multi-Objective PDE Constrained Optimizationfor a 250 MeV Injector

We present a PDE constrained multi-objective optimiza-tion model for the 250 MeV electron injector to be com-missioned at Paul Scherrer Institut. Realizing good beamquality (compact in phase space) and attaining the de-sign energy are crucial to achieve the desired performance.In this context, state of the art massively parallel multi-objective optimization algorithms will be instrumental forthe optimal design of the injector. We discuss suitablemulti-objective optimization algorithms and plans for theirimplementation.

Yves IneichenETHZPSI

[email protected]

Andreas AdelmannPaul Scherrer [email protected]

Peter ArbenzETH ZurichChair of Computational [email protected]

Costas BekasIBM ResearchZurich Research [email protected]

Alessandro CurioniIBM [email protected]

CP20

Sensitivity-Based Optimization of Navier-StokesProblems with Heat Transfer

This work presents the methodology of a sensitivity analy-sis utilizing the continuous sensitivity equation approachregarding laminar, incompressible fluid flows with heattransfer. The arising set of equations is solved with an effi-cient finite-volume solver on a block structured grid. Fur-thermore, the resulting sensitivities of the flow concerningchanges in boundary conditions such as velocities and tem-perature as well as geometric variations using NURBS arepresented via a generic testcase.

Johannes Siegmann, Julian Michaelis, Michael SchaeferFachgebiet Numerische BerechnungsverfahrenTU [email protected], [email protected], [email protected]

CP20

An Interior-Point Algorithm for Shakedown Anal-ysis of Large-Scale Engineering Structures

An interior-point algorithm for the computation of shake-down loads of large-scale engineering structures subjectedto varying thermo-mechanical loading is presented. Theaccording optimization problem is characterized by a largenumber of variables and constraints. Thus, the calculationcan be computationally expensive and time-consuming. Aselective algorithm is introduced to overcome this prob-lem by dynamic reduction of the entire system to criticalsubstructures. The method is illustrated by numerical ex-amples in mechanical engineering.

Jaan W. Simon, Dieter WeichertInstitute of General MechanicsRWTH Aachen [email protected], [email protected]

CP20

An Iterative Regularization Algorithm for Opti-mization in Parameters Identification Problems.

In this work we present an iterative regularization algo-rithm for solving a parameter identification problem rela-tive to a system of diffusion, convection and reaction equa-

92 OP11 Abstracts

tions (state equations). The parameters to be identified arethe diffusivity and reaction terms. The problem is solvedby means of a succession of nonlinear constrained opti-mization problems. The problems are ill-posed and needregularization. For each problem, the proposed algorithmcomputes the sequence of regularization parameters by us-ing the lagrangian dual formulation of the constrained op-timization problem. The state parameters are computedby truncated iterative solution of the inner system. Theeffectiveness of the method is evaluated on 1D and 2D testproblems with different levels of noise in the measurements.

Fabiana ZamaDepartment of Mathematics, University of [email protected]

Elena Loli PiccolominiDepartment of Mathematics,University of [email protected]

CP21

Scenario Decomposition of Risk-Averse MultistageStochastic Programming Problems

For a risk-averse multistage stochastic optimization prob-lem with a finite scenario tree, we introduce a new scenariodecomposition method and we prove its convergence. Themain idea of the method is to construct a family of risk-neutral approximations of the problem. The method isapplied to a risk-averse inventory and assembly problem.

Ricardo A. ColladoIOMS-Operations Management GroupStern School of Business, [email protected]

Andrzej RuszczynskiRutgers UniversityMSIS [email protected]

David PappRutgers Center for Operations [email protected]

CP21

Uncertainty Modeling for Robust Optimization

Polyhedral clouds have recently demonstrated strength indealing with higher dimensional uncertainties in robust op-timization, even in case of partial ignorance of statisticalinformation. However, in real-life applications the compu-tational effort to account for robustness, i.e., to find worst-case scenarios, should not exceed certain limitations. Wepropose a simulation-based approach for optimization overa polyhedron, inspired by the Cauchy deviates method.Thus we achieve a tractable method to compute worst-casescenarios with polyhedral clouds.

Martin FuchsCERFACSParallel Algorithms [email protected]

CP21

A Sparsity Preserving Stochastic Gradient Descent

Algorithm

In this paper, we propose new stochastic gradient descentalgorithms for solving convex composite optimization prob-lems. Our algorithms utilize a stochastic approximation ofthe gradient of the smooth component of objective func-tions in each iteration. We prove that the expectationand the variance of the solution errors converge to zeros.The convergence rates are proved using the arguments ofstochastic estimate sequences. When applied to regular-ized regression problems, our algorithms distinguish fromother stochastic gradient methods by preserving sparsitystructures in the solutions in all iterations.

Qihang LinCarnegie Mellon UniversityTepper School of [email protected]

Xi ChenCarnegie Mellon UniversitySchool of Computer [email protected]

Javier PenaCarnegie Mellon UniversityTepper School of [email protected]

CP21

Efficient Bayesian Updating of Parameters for Heatand Moisture Transport in Heterogenous Materials

The Bayes formula can be used to provide a reliable esti-mation of the probability distributions of heat and mois-ture transport in structures. It combines a priori infor-mation about material properties and measurment data.We present a new method to numericaly compute a Bayesupdate in a direct, fast and reliable manner. As an exam-ple we focus on the description of heterogeneous materialwhich includes the uncertainty in material parameters to-gether with its spatial fluctuations.

Bojana V. RosicInstitute of Scientific ComputingTU [email protected]

Hermann G. Matthies, Oliver PajonkInstitute of Scientific ComputingTechnische Universitat [email protected], [email protected]

ANNA Kucerova, JAN SykoraFaculty of Civil Engineering, Prague, Czech [email protected], [email protected]

CP21

Bundle Methods for Hydro Reservoir Managementwith Joint Chance Constraints

In the electrical industry, offer-demand equilibrium prob-lems for hydrothermal systems are often solved by usingprice decomposition techniques. In this setting, the partic-ular sub-problems optimizing one hydraulic valley are typi-cally large-scale combinatorial network flow problems. Thecombinatorial nature of such problems is due to complexdynamic constraints on the watershed controls. For thesereasons, such problems are often considered in a determin-

OP11 Abstracts 93

istic setting, even though reservoir streamflow is uncertainin practice. We propose to tackle uncertainty (in a contin-uous setting, without complex watershed constraints) byformulating the flow constraints using joint chance con-straints. We consider inflows following any causal timeseries model with Gaussian innovations. The sub-problemis convex, with probabilistic constraints defined in a highlydimensional cube that can be efficiently evaluated by theso-called Genz code. Since the cutting planes techniquetakes too many iterations to converge to an accurate solu-tion rapidly, we consider how to use a constrained variantof the bundle method, capable of handling inaccurate sub-gradient calculations. The approach is assessed on a real-size hydro-sub-problem typical of the French power mix.

Wim Van AckooijEDF R&DDepartment [email protected]

Rene HenrionWeierstrass InstituteBerlin, [email protected]

Claudia A. [email protected]

Riadh ZorgatiEDF R&DDepartment [email protected]

CP21

Approximate Dynamic Programming with BezierCurve Approximations for Top Percentage TrafficRouting

This study investigates the optimal routing strategy undermulti-homing where cost are computed with top-percentilepricing. This problem is stochastic and large. Solution ap-proaches based on Stochastic Dynamic Programming re-quire discretization in state space, which suffers from thecurse of dimensionality. To overcome this we use Approxi-mate Dynamic Programming to construct approximationsof value function, and develop Bezier Curves/Surfaces ag-gregation in time. This accelerates the efficiency of param-eter training, which makes the real-sized TpTRP tractable.

Xinan YangUniversity of [email protected]

Andreas GrotheySchool of MathematicsUniversity of [email protected]

CP22

Planning the Expansion of Railway Networks ANetwork Design Problem

We present a mixed integer model to support the decisionprocess at Deutsche Bahn, the largest European RailwayCompany, on how to optimally invest their annual bud-

get in expanding the railway infrastructure to cope withfuture demands. Our model views the problem as a net-work design problem with an underlying routing problem.It considers a long-term planning horizon, where expensivemeasures can be stretched over several years. We also givecomputational results on real-world instances.

Andreas BarmannFriedrich-Alexander-Universitat [email protected]



CP22

Optimization of Gas and Water Supply Networks

The optimal control of gas and water supply networks is achallenging task. The dynamics in both types of networksare governed by hyperbolic systems of PDEs. Additionally,components like compressor/pumping stations and valvesintroduce binary decisions in the optimal control problem.A key ingredient is to efficiently solve the underlying simu-lation task with reliable error bounds. Therefor, we applyadjoint-based error estimators. This approach also pro-vides gradient information for the optimization.

Pia Domschke, Oliver KolbTU [email protected],[email protected]

Jens LangDepartment of MathematicsDarmstadt University of [email protected]

CP22

Bounded Diameter Minimum Spanning Trees: ANew Approach Combining Branch-and-Bound andEnumeration Algorithms

We address the problem of computing diameter-constrained minimum spanning trees. So far this problemhas mainly been investigated for the case of unit length. Weaim at exploring the more general case where the lengthof the edges can be any number. To approach this prob-lem, we develop a new algorithm combining branch-and-bound procedures with enumeration algorithms for span-ning trees. The latter can be used for producing upper andlower bounds. Computational experiments are reported.

Ute GuentherTU DarmstadtFB [email protected]


CP22

A Polyhedral Approach for Solving Two-Facility

94 OP11 Abstracts

Network Design Problem

The paper studies the problem of designing telecommu-nication networks using transmission facilities of two dif-ferent capacities. We fully characterize and enumerate allthe extreme points of the 3-node subproblem polyhedron.A new approach for computing facets is introduced and anew family of facets is identified. The 3-partition basedfacets strengthen the linear programming formulation toa great extent. Computational results show these facetssignificantly reduce integrality gap and size of the branch-and-bound tree.

Faiz Hamid, Yogesh K. AgarwalIndian Institute of Management, Lucknow, [email protected], [email protected]

CP22

On Clearing Coupled Day-Ahead Electricity Mar-kets

The European power grid is divided into several marketareas connected by power lines with restricted transmissioncapacity. Hence supply and demand of adjacent areas cannot always be balanced. The goal of a day-ahead auction isto determine prices and cross border flow maximizing theeconomic surplus of all participants. Also the transmissionand distribution losses must be considered. A MIQP isused to model this challenge.

Johannes C. Muller, Alexander MartinUniversity of [email protected],[email protected]


CP23

Model Hierarchy Based Multilevel SQP-Methodsfor PDAE-Constrained Optimal Control Problemswith Application to Radiative Heat Transfer

We present a multilevel-SQP-method, applied to a radia-tive heat transfer problem in glass manufacturing. To han-dle the direction- and frequency-dependent radiation, wemake use of series expansion and discretize the continu-ous frequency spectrum into different bands. The focus ison the multilevel strategy, which is based on a hierarchyof mathematical models and a sequence of adaptive space-time discretizations with increasing accuracy. Mathemat-ical models are obtained by varying the expansion orderand the number of frequency bands.

Debora CleverGraduate School CE,Technische Universitat [email protected]

CP23

Solving the Einstein Constraint Equations UsingBarrier Methods

The Einstein field equations for general relativity describehow gravity interacts with matter and energy. The equa-tions are a system of ten coupled equations, comprised ofsix evolution equations and four constraint equations. Theconstraint equations must be enforced at each time step

when solving the evolution equations. Implicit in the Ein-stein constraint equations is an additional simple inequal-ity. We look at solving these equations using barrier meth-ods together with a traditional finite element approach.

Jennifer ErwayWake Forest [email protected]

CP23

Nonlinear Optimum Experimental Design for In-dustrial Processes

Dynamical processes from industry can be modeled by sys-tems of differential equations. These models have to bevalidated by estimation of unknown parameters from ex-perimental data. Designing experiments which minimizethe uncertainty of the parameters leads to intricate non-standard optimal control problems. This talk presents re-cent advances in the formulation and solution methods ofthese problems including adjoint differentiation, multipleshooting and an online approach. Examples from the prac-tice of our industrial partners are given.

Stefan KorkelInterdisciplinary Center for Scientific ComputingHeidelberg [email protected]

CP23

Optimization under Uncertainty of a Wind Turbine

In this work a model of wind turbine is presented, consid-ering a variable pitch and rotational speed control, fluid-structural interaction and acoustics. Hence a typical tur-bine design is analyzed under uncertainty (e.g. wind speed)by the use of a Simplex Elements Stochastic Collocation(SESC) method, based on adaptive grid refinement of asimplex elements discretization in probability space. Theapproach is equally robust as Monte Carlo (MC) simulationin terms of the Extremum Diminishing (ED) robustnessconcept. In conclusion a process of shape optimization un-der uncertainty via genetic algorithms will be considered.

Giovanni Petrone, Carlo De NicolaUniversita degli Studi di Napoli Federico [email protected], [email protected]

Domenico QuagliarellaCentro Italiano Ricerche [email protected]

Gianluca IaccarinoStanford [email protected]

Jeroen WitteveenStanford UniversityCenter for Turbulence [email protected]

CP23

Optimum Experimental Design for Advection-Diffusion-Reaction Problems

Optimum Experimental Design is the task of finding anexperiment that behaves best in the sense of reducing un-certainties in the parameters that are to be estimated from

OP11 Abstracts 95

it. With PDE constraints new challenges arise for this op-timization problem. We want to present an adjoint modefor the costly gradient calculation following Automatic Dif-ferentiation principles and discuss questions for the placingof measurement points in time and space.

Andreas SchmidtInterdisciplinary Center For Scientific Computing,[email protected]

CP24

Multilevel Shape Optimization for the InstationaryNavier-Stokes Equations

We consider shape optimization problems governed by theinstationary incompressible Navier-Stokes equations. Weuse an approach based on transformations of a referencedomain which is very flexible and allows arbitrary typesof parametrizations. Shape derivatives are derived in acontinuous adjoint approach. Our focus is on the efficientnumerical solution of discretized shape optimization prob-lems. This is achieved by using multilevel optimizationwith adaptivity based on goal oriented error estimators.Numerical results are presented.

Christian BrandenburgTU [email protected]


CP24

New Discrete Approach for Topology-Optimizationin Mechanical Engineering

The new discrete approach combines simple but very pow-erful ideas for topology optimizations. No gradient infor-mation is necessary to reduce and add material. Here acontroller-mechanism is used. Only the changes of targetfunction, e.g. displacements or reaction forces, are nec-essary to solve the optimization problem. All non-lineareffects in FEM-simulations can be considered. The sim-ple and basic approach solves the optimization problems(academic examples as well as industrial problems) in anamazing way.

Sierk [email protected]

CP24

Actuator Positioning in Truss Topology Design

The aim is to find the optimal topology of a truss andthe optimal positioning of the actuators within this trussby solving just one optimization problem. The actuatorsare modelled as binary variables so we get a MINLP. Weare going to compare different models, such as a semidef-inite MIP, a MIP and a quadratic MIP. For solving theMISDP we put a branch-and-bound-framework togetherwith a SDP-solver. First computational results are pre-sented.

Sonja Friedrich

TU Darmstadt, Department of MathematicsDiscrete [email protected]

Lars ScheweFriedrich-Alexander-Universitat Erlangen Nurnberg,Department Mathematik, [email protected]

Jakob SchelbertFriedrich-Alexander-Universitat Erlangen-NurnbergDepartment Mathematik, [email protected]

Kai HabermehlTU Darmstadt, Department of MathematicsNonlinear [email protected]

CP24

Nonlinear Elastic Shape Optimization and Uncer-tain Loading

Shape optimization of mechanical devices is investigatedin the context of large, geometrically strongly nonlineardeformations and nonlinear hyperelastic constitutive laws.A weighted sum of the structure compliance, its weight,and its surface area are minimized. The resulting nonlin-ear elastic optimization problem differs significantly fromclassical shape optimization in linearized elasticity. In-deed, there exist different definitions for the compliance:the change in potential energy of the surface load, thestored elastic deformation energy, and the dissipation as-sociated with the deformation. Furthermore, elasticallyoptimal deformations are no longer unique so that one hasto choose the minimizing elastic deformation for which thecost functional should be minimized, and this complicatesthe mathematical analysis. Additionally, along with thenon-uniqueness, buckling instabilities can appear, and thecompliance functional may jump as the global equilibriumdeformation switches between different bluckling modes.This is associated with a possible non-existence of optimalshapes in a worst-case scenario.In this paper the sharp-interface description of shapes isrelaxed via an Allen–Cahn or Modica–Mortola type phase-field model, and soft material instead of void is consideredoutside the actual elastic object. An existence result foroptimal shapes in the phase field as well as in the sharp-interface model is established, and the model behaviorfor decreasing phase-field interface width is investigated interms of Γ-convergence. Computational results are basedon a nested optimization with a trust-region method as theinner minimization for the equilibrium deformation and aquasi-Newton method as the outer minimization of the ac-tual objective functional.

Martin RumpfRheinische Friedrich-Wilhelms-Universitat BonnInstitut fur Numerische [email protected]

Benedikt WirthRheinische Friedrich-Wilhelms-Universitat [email protected]

Patrick PenzlerUniversitat [email protected]

96 OP11 Abstracts

CP24

An Approximation Technique for Robust ShapeOptimization

We present a second-order approximation for the robustcounterpart of general nonlinear programs with state equa-tion given by a PDE. We show how the approximated ro-bust counterpart can be formulated as trust-region problemwhich can be solved efficiently using adjoint techniques.This method is applied to shape optimization in structuralmechanics in order to obtain optimal solutions that arerobust with respect to uncertainties in acting forces andother quantities. Numerical results are presented.

Adrian SichauTU Darmstadt, Department of MathematicsResearch Group Nonlinear [email protected]


CP25

A Family of Dantzig-Wolfe Type DecompositionAlgorithms for Variational Inequality Problems.

We present a family of algorithms for variational inequal-ities based on ideas of Dantzig-Wolfe decomposition forlinear programming. Constraints of the problem are sep-arated into ”hard” and ”easy”. At each iteration, twosubproblems are solved. One deals with easy constraints,dualizing hard using Lagrange multipliers provided by thesecond subproblem. Second subproblem involves hard con-straints, reducing variables restricting to convex hull of pre-viously generated points. Various approximations of theconstraints and VI mapping are allowed.

Juan Pablo Cajahuanca LunaInstituto de Matematica Pura e Aplicada [email protected]

Mikhail V. SolodovInst de Math Pura e [email protected]


CP25

The Split Variational Inequality Problem

We propose a new variational problem which we call theSplit Variational Inequality Problem (SVIP). It entailsfinding a solution of one Variational Inequality Problem(VIP), the image of which under a given bounded lineartransformation is a solution of another VIP. This problemis interesting not only from the theoretical point of viewbut also because of its potential applications. We constructiterative algorithms that solve such problems, under rea-sonable conditions, in Hilbert space and then discuss spe-cial cases, some of which are new even in Euclidean space.

Aviv GibaliThe Technion - Israel Institute of Technologyaviv [email protected]

Yair CensorUniversity of HaifaDepartment of [email protected]

Simeon ReichDepartment of Mathematics,The Technion - Israel Institute of [email protected]

CP25

Second-Order Cone Based Reformulation for Ro-bust Wardrop Equilibrium Problems

In this paper, we define the notion of robust Wardrop equi-librium for traffic model with uncertain data. Particularly,we show that the problem of finding such an equilibriumcan be cast as a second-order cone complementarity prob-lem, when the uncertain data are expressed by means ofEuclidean norms. We also report some numerical resultsto observe the behavior of obtained equilibria with variouschoices of uncertainty structures.

Yoshihiko Ito, Hitoshi TakahashiKyoto [email protected], [email protected]

Shunsuke HayashiDept of Applied Mathematics and PhysicsGraduate School of Informatics, Kyoto [email protected]

CP25

Interior-Point Method for Nonlinear Programmingwith Complementarity Constraints

We propose an algorithm for solving nonlinear program-ming problems with complementarity constraints, whichis based on the interior-point approach. Main theoreti-cal results concern direction determination and step-lengthselection. We use an exact penalty function to removecomplementarity constraints. Thus a new indefinite linearsystem is defined with a tridiagonal low-right submatrix.Furthermore, new merit function is defined, which includesbarrier, exact penalty, and augmented Lagrangian terms.

Ladislav Luksan, Ctirad Matonoha, Jan VlcekInstitute of Computer ScienceAcademy of Sciences of the Czech [email protected], [email protected], [email protected]

CP25

Two Strong Convergence Theorems for BregmanStrongly Nonexpansive

We study the convergence of two iterative algorithmsfor finding common fixed points of finitely many Breg-man strongly nonexpansive operators in reflexive Banachspaces. Both algorithms take into account possible compu-tational errors. We establish two strong convergence theo-rems and then apply them to the solution of convex feasi-bility, variational inequality and equilibrium problems.

Shoham SabachTechnion - Israel institute of [email protected]

OP11 Abstracts 97

CP25

Control of Variational Inequalities

We consider the problem of ”critical excitation” (i.e., thelowest energy input connecting prescribed states within agiven time span) for the variational inequality describing asingle degree of freedom elasto-plastic oscillator. This is anoptimal control problem for a non smooth state evolution.We obtain Pontryagin’s necessary condition of optimality.An essential difficulty lies with the non continuity of ad-joint variables. We define an algorithm which leads to theoptimal control.

Janos TuriUniversity of Texas at [email protected]

Alain BensoussanUniversity of Texas at Dallasand the Hong Kong Polytechnic University, Hong [email protected]

CP26

A Bound for Super-Resolution Power of Compres-sive Sensing Imaging Systems

Compressive Sensing (CS) has proven a robust and high-resolution method for Synthetic Aperture Radar Tomogra-phy (TomoSAR) from space. For the typical satellite orbitconfigurations, resolution is a crucial aspect. This paperquantifies the super-resolution power of CS, i.e. the min-imum separable distance between two point scatterers, asa function of SNR, number of measurements N, and am-plitude ratio of the scatterers for the typical low SNR andlow N cases of TomoSAR.

Richard BamlerGerman Aerospace Center (DLR)Remote Sensing Technology Institute (IMF)[email protected]

Xiao Xiang ZhuTechnische Universitat Munchen (TUM)Lehrstuhl fur Methodik der [email protected]

CP26

Sparsity-Regularized Methods for Practical Opti-cal Imaging

Traditionally, optical sensors have been designed to col-lect the most directly interpretable measurements possi-ble. However, recent advances in image reconstructionand compressed sensing indicate that substantial perfor-mance gains may be possible in many contexts via com-putational methods. In this talk, we explore the potentialof physically realizable systems for acquiring “incoherent”measurements. Specifically, we describe how given a fixedsize photodetector, compressive measurements with sophis-ticated optimization algorithms can significantly increaseimage quality and resolution.

Roummel F. MarciaSchool of Natural SciencesUniversity of California, [email protected]

CP26

Efficient Methods for Least-Norm Regularization

We consider the problem: min ‖x‖2 s.t. ‖Ax − b‖2 ≤ ε,where A is an m × n matrix, b is an m × 1 data vectorcontaining errors (noise), and ε is an upper bound on thenorm of the noise. This problem arises, for example, inthe regularization of discrete forms of ill-posed problems.We present two classes of methods: a Newton iterationfor small, dense problems, and two matrix-free algorithmsfor the large-scale case. We present numerical results thatdemonstrate that the new methods are accurate, efficient,and robust

Marielba RojasDelft University of [email protected]

Danny C. SorensenRice [email protected]

CP26

The Sl1mmer Algorithm for Spectral EstimationWith Application to Tomographic Sar Inversion

We introduce SL1MMER, a spectral estimation algorithmbased on L1-norm minimisation, model order selection andfinal parameter estimation. It combines the advantages ofcompressive sensing with the amplitude and phase accu-racy of linear estimators. Our target application is differen-tial Synthetic Aperture Radar (SAR) tomography. We willalso show that by means of our proposed time warp methodthe tomographic imaging equation with an M-componentmotion model can be rewritten as an M+1-dimensionalspectral estimation problem.

Xiao Xiang Zhu

Technische Universitat Munchen (TUM)Lehrstuhl fur Methodik der [email protected]

Richard BamlerGerman Aerospace Center (DLR)Remote Sensing Technology Institute (IMF)[email protected]

CP27

Decomposition Methods for Two-Stage Problemswith Stochastic Dominance Constraints

We consider two-stage stochastic optimization problemswith risk control by a stochastic dominance constrainton the recourse function. We propose two decompositionmethods to solve the problems and prove their convergence.Our methods exploit the decomposition structure of theexpected value two-stage problems and approximate thestochastic dominance constraints. The dominance relationis represented by the Lorenz functions or by the expectedexcess functions of the random variables involved. Numer-ical results confirm the efficiency of the methods.

Darinka DentchevaDepartment of Mathematical SciencesStevens Institute of [email protected]

Gabriela MartinezStevens Institute of Technology

98 OP11 Abstracts

[email protected]

CP27

A Sampled Fictitious Play Based Learning Algo-rithm for Infinite Horizon Markov Decision Pro-cesses

Using Sampled Fictitious Play (SFP) concepts, we developa learning algorithm for solving discounted homogeneousMarkov Decision Problems where the transition probabil-ities are unknown and need to be learned via simulationor direct observation of the system in real time. Thus,SFP estimates and simultaneously updates the unknowntransition probabilities, optimal value and optimal actionin observed state. We prove convergence of the algorithmand compare its performance with other adaptive learningmethods.

Marina A. EpelmanUniversity of MichiganIndustrial and Operations [email protected]

Esra SisikogluUniversity of MissouriIndustrial & Manufacturing Systems [email protected]

Robert L. SmithIndustrial and Operations EngineeringUniversity of [email protected]

CP27

Optimizing Stochastic Mixed-Integer Problemswith Application in Energy Production

We consider a stochastic mixed-integer model, where un-certainty is described by a scenario tree. To solve thisblock-structured problem, we apply a decomposition ap-proach which exploits the problem specific structure. Onthis basis a branch-and-bound algorithm is used to ensurefeasibility and solve the problem to global optimality. Asan application, we present a power generation problem withfluctuating, regenerative power supply.

Debora Mahlke, Andrea ZelmerFriedrich-Alexander-Universitat Erlangen-NurnbergLehrstuhl fur [email protected],[email protected]


CP27

Stochastic Network Design with Random Demandsand Arc Capacities.

Networks are considered where the demands at the nodesand some of the arc capacities are random variables thathave joint normal distribution. A network design problemis formulated where a probabilistic constraint assures theexistence of a feasible flow by a large probability. Thenumerical solution is obtained using several methods:themethod of Prekopa that combines a cutting plane methodwith supporting hyperplane method; dynamic quadratic

approximation method, so called ”supporting hyperbolae”.

Olga MyndyukRutgers University, [email protected]

Andras PrekopaRutgers UniversityRutgers Center for Operations [email protected]

CP27

Partly Inexact Bundle Methods for Two-StageStochastic Linear Programming

For two-stage stochastic linear programs, we considerpartly inexact bundle methods, corresponding to a regular-ized Benders decomposition that can handle inexactness inthe second-stage subproblems solution. Subproblems aresolved exactly only at some specific points, when inaccu-racy is deemed too large. The remaining subproblems so-lution is approximated by means of previously generatedvertices. We analyze two alternatives, derived the proximaland level bundle methods, and assess their performance ona battery of two-stage problems from the stochastic pro-gramming literature.

Welington OliveiraFederal University of Rio de [email protected]

Claudia A. [email protected]

Susana ScheimbergFederal University of Rio de [email protected]

CP27

Risk-Averse Dynamic Programming for StochasticShortest Path Problems

We introduce the concept of a Markov risk measure and weuse it to formulate a risk-averse version of the undiscountedstochastic shortest path problem in an absorbing Markovchain. We derive risk-averse dynamic programming equa-tions and we show that a randomized policy may be strictlybetter than deterministic policies, when risk measures areemployed.

Andrzej Ruszczynski, Ozlem CavusRutgers [email protected], ozlem [email protected]

CP28

Bounds for the Nonnegative Rank Using a Geo-metric Interpretation

The minimum number of nonnegative rank-one factorssumming to a given matrix is its nonnegative rank. De-termining this rank and the corresponding factors is com-putationally difficult but has many applications, e.g., ingraph theory, or to characterize the minimal size of anyLP extended reformulation of a combinatorial optimizationprogram. In this talk, we shed new light on this problem

OP11 Abstracts 99

using a geometric interpretation involving polyhedral com-binatorics, leading to improved upper and lower bounds.

Nicolas GillisUniversite catholique de LouvainCenter for Operation Research and [email protected]

Francois GlineurUniversite catholique de LouvainCenter for Operations Research and [email protected]

CP28

Manifold Learning by Semidefinite Facial Reduc-tion

We propose a new semidefinite programming formulationfor nonlinear dimensionality reduction by manifold learn-ing. By observing that the structure of a large chunk ofthe data can be preserved as a whole, we are able to usea recent result on semidefinite facial reduction [Krislockand Wolkowicz, 2010] to significantly reduce the size andthe number of constraints of the semidefinite programmingproblem, allowing us to solve much larger problems thanpreviously possible.

Nathan KrislockINRIA Grenoble [email protected]

Babak AlipanahiDavid R. Cheriton School of Computer ScienceUniversity of [email protected]

Ali GhodsiUniversity of [email protected]

CP28

Robust Covariance Estimation Using Mathemati-cal Programming

The outlier detection problem and the robust covarianceestimation problem are often interchangeable. Withoutoutliers, the classical method of Maximum Likelihood Es-timation (MLE) can be used to estimate parameters of aknown distribution from observational data. When outliersare present, they dominate the log likelihood function caus-ing the MLE estimators to be pulled toward them. Manyrobust statistical methods have been developed to detectoutliers and to produce estimators that are robust againstdeviation from model assumptions. However, the exist-ing methods suffer either from computational complexitywhen problem size increases or from giving up desirableproperties, such as affine equivariance. An alternative ap-proach is to design a special mathematical programmingmodel to find the optimal weights for all the observations,such that at the optimal solution, outliers are given withsmaller weight and can be detected. This method pro-duces a covariance estimator that has the following prop-erties: First, it is affine equivariant. Second, it is compu-tationally efficient even for large problem sizes. Third, iteasy to incorporate prior beliefs into the estimator by usingsemi-definite programming. The accuracy of this methodis tested for different contamination models, including the

most recently proposed ones.

Tri-Dung NguyenUniversity of SouthamptonSchool of [email protected]

CP28

Learning over Manifolds via Iterative Projection

The problem of recovering an unknown signal belonging toa manifold from linear measurements has multiple applica-tions, one important one being imaging. In this work weintroduce an algorithm known as Manifold Iterative Pro-jection to solve the problem of recovering an unknown sig-nal from a manifold using linear measurements. We showthat when the linear measurement operator operates be-nignly on the manifold, the algorithm recovers the un-known signal. We also extend the analysis to the casewhere the signal varies slowly with time on the manifold,and show that using the algorithm one can track the time-varying signal. For well-behaved manifolds, random (Gaus-sian) matrices are suitable measurement operators, and thesample-complexity and time-complexity can be character-ized in terms of the geometric properties of the manifold.We illustrate the algorithm on several examples.

Parikshit [email protected]

Venkat ChandrasekaranMassachusetts Institute of [email protected]

CP29

Extension of the Semidefinite Characterization ofSum of Squares Functional Systems to AlgebraicStructures

Nesterov has shown that the cone of functions that canbe expressed as sums of squares of functions in a finitedimensional linear functional space can be represented bypositive semidefinite matrices. We extend this result toany abstract algebraic system. Our extension is particu-larly useful for formally real algebras. As a result we unifysome results under this framework. A noted example isthe characterization of polynomials (ordinary, exponentialand trigonometric) which take only positive semidefinitevalues in Jordan algebras. Using Youla’s theorem we showthat such sets of polynomials are SDP-representable. Wealso extend our results by defining the notion of A-sdp ma-trices, which are matrices whose entries are from an alge-bra (A, �). Finally, we explore some concrete applicationsof these characterizations in statistical function estimationand some problems in shape optimization.

Farid AlizadehRUTCOR and School of Business,Rutgers [email protected]


CP29

A Geometric Theory of Barriers in Conic Opti-

100 OP11 Abstracts

mization

We interpret barriers in conic optimization as Lagrangiansubmanifolds of some universal para-Kahler space form andestablish close links to centro-affine hypersurface geometry.As an application, we construct a universal self-concordantbarrier which, in contrast to the classical universal barrier,is invariant with respect to duality and the operation oftaking products of cones. This barrier corresponds to theminimal Lagrangian submanifolds, or to hyperbolic affinehyperspheres in centro-affine geometry.

Roland HildebrandLaboratoire Jean KuntzmannUniversity Grenoble 1 / [email protected]

CP29

A Globally Convergent Algorithm for Semi-InfinitePrograms with an Infinite Number of Conic Con-straints

The semi-infinite program (SIP) is normally representedwith infinitely many inequality constraints, and has beenmuch studied so far. However, there have been only afew studies on the SIP involving conic constraints suchas second-order cone constraints, even though it has im-portant applications such as Chebychev-like approximationand filter design. In this paper, we focus on the SIP withinfinitely many conic constraints, called the SICP for short.We show that, under an appropriate constraint qualifica-tion, an optimum of the SICP satisfies the Karush-Kuhn-Tucker conditions that can be represented with only a fi-nite subset of the conic constraints. Next we provide analgorithm for solving the SICP and show that it generatesiterates converging to a solution of the SICP under somemild assumptions. Moreover, we report some numericalexperiments.

Takayuki OkunoDepartment of Applied Mathematics and PhysicsGraduate School of Informatics Kyoto Universityt [email protected]

Shunsuke HayashiDept of Applied Mathematics and PhysicsGraduate School of Informatics, Kyoto [email protected]

Masao FukushimaDepartment of Applied Mathematics and PhysicsGraduate School of Informatics Kyoto [email protected]

CP29

Optimizing Extremal Eigenvalues of the WeightedLaplacian of a Graph

In order to better understand spectral properties of theLaplace matrix of a graph, we optimize the edge weights soas to minimize the difference of the maximal and the secondsmallest eigenvalue of the weighted Laplacian. Using asemidefinite programming formulation, the dual programallows to interpret the dual solutions living in the optimizedeigenspaces as a graph realization. We study connectionsbetween structural properties of the graph and geometricalproperties of graph realizations.

Susanna Rei

Chemnitz University of [email protected]


CP29

Riemannian Optimization for Rank-ConstrainedMatrix Problems

We present a Riemannian framework for solving optimiza-tion problems involving a rank constraint. The proposedmethods exploit that the set of n × n matrices of fixed

rank k, denoted M‖\, form a smooth embedded submani-

fold of Rn×n. This enables the use of so-called Riemannianoptimization, the generalization of classic optimization to

Riemannian manifolds. Since the manifold M‖\ is of di-

mension O(nk), these algorithms are inherently defined ona lower dimensional search space compared to the full-rankcase when k � n. Furthermore, the framework is flexibleenough to allow for second-order algorithms, precondition-ing and multilevel optimization. We illustrate this withtwo applications: Lyapunov equations involving PDEs andlow-rank matrix completion.

Bart VandereyckenKatholieke Universiteit [email protected]

CP30

Finite Element Error Estimates on the Boundaryand Its Application To Optimal Control

Finite element error estimates in the L2-norm on theboundary are proved for elliptic boundary value problemsin polygonal domains. Local mesh grading is used in thevicinity of corners with interior angle greater than 2π/3.The result is used to estimate the discretization error ofelliptic linear-quadratic Neumann boundary control prob-lems with pointwise inequality constraints on the control.

Thomas ApelUniversitat der Bundeswehr [email protected]

Johannes PfeffererUniBw [email protected]

Arnd RoschUniversity of [email protected]

CP30

A Finite Element Method Based Numerical Algo-rithm for Calculus of Variations Problems Derivedfrom Gateaux First Variation

A standard calculus of variations problem consists in min-imising a given objective functional, subject to Dirichletboundary conditions. Stationary points of this problem areobtained by imposing the Gateaux first variation necessarycondition. A corresponding numerical scheme is attainedby approximating the problem’s true solution, expressingthe interpolant as a linear combination of cubic spline ba-

OP11 Abstracts 101

sis functions. Different numerical integration rules for theintegrals intervening in Gateaux first variation expressionare applied.

Ana Garcia-BousoUniversidad Rey Juan CarlosStatistics and Operations Research [email protected]

Alberto Olivares, Ernesto StaffettiUniversidad Rey Juan Carlos (Madrid)Statistics and Operations Research [email protected], [email protected]

CP30

Multivariate Shape-Constrained Estimation UsingPolynomial Splines

We present a solution to multivariate function estimationproblems with shape constraints on the estimator. We ap-ply tools from polynomial programming and decompositionmethods. The estimator is a multivariate spline, for whichmost natural shape constraints are intractable, hence weconsider tractable restrictions involving weighted-sum-of-squares cones. The size of these problems often makes thedirect solution of the models impossible, hence the need tocombine the conic programming technique with decompo-sition methods.


Farid AlizadehRUTCOR and School of Business,Rutgers [email protected]

CP30

Numerical Explorations of Benford DistributedRandom Variables

A random variable is Benford distributed if the occur-rence frequency of its most significant digit is p(d) =log10(1 + 1/d). Using numeric data from 2-d relativisticgas simulations, we observed that the generalized relativis-tic equipartition terms are Benford distributed. They arealso base and scale invariant. Because the equipartitionterms are nonlinear functions of non-uniform distributedrandom variables, we expect that the exponentiation the-orem of Adhikari and Sarkar be extended to non-uniformprobability distribution functions as well.

Constantin N. Rasinariu, Azar KhosravaniDepartment of Science and MathematicsColumbia College [email protected], [email protected]

CP30

Optimal Input Design with B-Splines: Linear Ver-sus Semidefinite Programming

Input design is considered for linear controllable systemsby means of a B-spline parametrization of the flat output.Actuator and state constraints are satisfied continuouslyin time by either conservative linear or exact semidefiniteconstraints on the spline coefficients resulting in a linear orsemidefinite program in which both the spline coefficients

and the knot locations are optimized simultaneously. Toillustrate and compare both approaches, time optimal in-puts are calculated for an overhead crane.

Wannes Van LoockKatholieke Universiteit LeuvenDepartment of Mechanical Engineering, division [email protected]

Goele Pipeleers, Jan SweversKatholieke Universiteit [email protected],[email protected]

CP31

Solving DFO Non Convex Subproblems with aGlobal Optimizer

The SQA (Sequential Quadratic Approximation) is a con-strained derivative-free algorithm developed at IFPEN. Inthe minimization stage, quadratic subproblems, not nec-essarily convex, subjected to bound and quadratic con-straints are solved using a standard SQP algorithm. Dueto the non-convexity issue, subproblem solutions computedthrough the local SQP algorithm may only be local solu-tions. This motivates our choice to use GloptiPoly, a globaloptimizer for polynomial optimization for solving quadraticsubproblems. In order to integrate GloptiPoly as the sub-problem solver, it was tested for some quadratic problemsof the Hock Shitkowski benchmark. Then, it was pluggedin SQA as the quadratic subproblem solver for the More &Wild benchmark. Finally, GloptiPoly was used for solvinga real engine calibration problem. Comparisons of Glop-tiPoly with standards SQP methods and multistart oneswill be given for the More & Wild benchmark and the cal-ibration problem, respectively.

Frederic DelbosIFP Energies [email protected]

Laurent DumasUniversite de [email protected]

Eugenio EchagueIFP energies [email protected]

CP31

Estimating Parameters in Optimal Control Models

We consider numerical methods for identifying models thatdescribe dynamical processes that can be assumed to beoptimal, such as gaits of cerebral palsy patients. Thisleads to challenging parameter estimation problems whoseconstraints are constrained optimal control problems. Wepresent a multiple shooting approach to discretize this hi-erarchical optimization problem and discuss methods totreat the resulting problem: a Gauß-Newton approach, abundle method, and a derivative-free technique. Numericalresults are provided.

Kathrin HatzInterdisciplinary Center for Scientific Computing (IWR)University of Heidelberg, [email protected]

Johannes Schloeder

102 OP11 Abstracts

Interdisciplinary Center for Scientific Computing (IWR)University of [email protected]


Sven LeyfferArgonne National [email protected]

CP31

Optimal Control of Hydroforming Processes

We consider optimal control problems for quasi-staticelastoplasticity with linear hardening. As a first stepderivative free optimization algorithms were used to con-trol the blank holder force and the fluid pressure, which aretypical control variables. The commercial FEM-softwareABAQUS is invoked for the simulations. Because of thehuge computational effort of the simulation, optimizationalgorithms based on reduced models are under investiga-tion. Numerical results for the hydroforming process ofsheet stringers will be presented.

Daniela KollerTU [email protected]


CP31

Derivative-free Methods for Large Nonlinear DataAssimilation Problems

To estimate the state of the ocean and of the atmosphere,very large nonlinear least-squares problems have to besolved. These problems involve a model operator whichintegrates a set of partial differential equations describingthe evolution of the system. Evaluating the derivatives ischallenging, as one needs to compute the Jacobian of themodel operator and its transpose, which implies the deriva-tion of a tangent linear and adjoint codes. In this talk, wepresent a derivative-free alternative based on the solutionof subproblems in well-choosen small subspaces.

Patrick LaloyauxUniversity of [email protected]

MS1

A Variational Inequality Approach for the Evolu-tion of Heterogeneous Materials

We aim to predict the evolution of microstructure in het-erogeneous materials, as appears, for example, in mate-rials that are submitted to radiation for long periods oftime. Such phenomena can be modeled by phase field ap-proaches with double obstacle potentials. Such formula-tions result in differential variational inequalities. We dis-cuss approaches for solving the large-scale variational in-equalities that result from spatial discretization combined

with time-stepping approaches.

Mihai Anitescu, Jungho Lee, Lois Curfman McInnes,Todd MunsonArgonne National LaboratoryMathematics and Computer Science [email protected], [email protected],[email protected], [email protected]

Barry F. SmithArgonne National LabMCS [email protected]

Lei WangUniversity of [email protected]

MS1

Extended Mathematical Programming: Multi-agent Modeling Simplified

We present the GAMS Extended Mathematical Program-ming framework (EMP). This new tool enables multi-agentmodels to be formulated in terms of individual agents, e.g.,optimization/complementarity models, and the structureand relationships that connect them, e.g. via a Nash gameor a leader-follower structure. The JAMS solver automati-cally reformulates the problem to create an equivalent buttractable model, solves it, and brings back the solution tothe EMP framework. Several examples are furnished forillustration.

Steven DirkseGAMS Development Corp.Washington [email protected]

Michael C. FerrisUniversity of WisconsinDepartment of Computer [email protected]

Jan-H. Jagla, Alex MeerausGAMS Development Corp.Washington [email protected], [email protected]

MS1

On C-stationarity for Parabolic MPECs

A constraint-relaxation technique for a class of optimalcontrol problems for parabolic variational inequalities isconsidered. The relaxed problem can be treated by well-known results from optimization in Banach space andyields, upon passing to the limit in the relaxation parame-ter, a weak form of C-stationarity for the original problem.The theoretical results are illustrated by numerical tests.

Michael HintermuellerHumboldt-University of [email protected]

MS1

Semismooth New-ton Methods for Quasi-Variational Inequalities of

OP11 Abstracts 103

Elliptic Type and Applications

A problem arising from a nonlinear elliptic quasi-variational inequality (QVI) with gradient constraints isconsidered. We address the existence of solutions based ona penalization approach and a fixed point iteration withoutresorting to Mosco convergence. The numerical approxi-mation of the solution is done by developing a semismoothNewton strategy in combination with the fixed point itera-tion in function space. Numerical examples related to thep-Laplacian and a superconductivity model will be treated.

Carlos N. RautenbergDepartment of Mathematics and Scientific ComputingKarl-Franzens University of [email protected]

MS2

Polynomial Descriptions of Special Classes of Semi-algebraic Sets

Bosse, Groetschel and Henk asked whether an arbitraryd-dimensional polytope can be described by d polynomialinequalities, i.e., in the form p1 ≥ 0, . . . , pd ≥ 0, wherep1, . . . , pd are d-variate polynomials. This question is an-swered in positive (in a joint work with Ludwig Brocker)and the corresponding theorem is also extended to the caseof unbounded polyhedra. In this talk I will sketch the proofand present some related problems.

Gennadiy AverkovUniversity of [email protected]

MS2

Spectrahedra and Determinantal Representationsof Polynomials

Spectrahedra are the feasible sets of semidefinite optimiza-tion problems. It is an important problem to characterizesets that are spectrahedra. The algebraic problem behindthis geometric question is to represent polynomials as de-terminants of linear matrix polynomials. I will discuss pos-itive and negative results concerning this problem.

Tim NetzerUniversity of [email protected]

MS2

Algebraic Certificates for Global Optimization andGeneralized Critical Values

We consider the problem of computing algebraic certifi-cates certifying lower bounds for the global infimum a mul-tivariate polynomial subject to equality constraints satisfy-ing transversality assumptions. Following a previous workof Demmel, Nie and Sturmfels involving sums-of-squaresdecompositions modulo gradient ideals, Nie has recentlyestablished the existence of SOS certificates modulo gen-eralized gradient ideals and convergence results in the casewhere the infimum is a minimum. Following an idea intro-duced by Schweighofer which consists in considering largervarieties than the ones defined by gradient ideals, we pro-vide existence results for algebraic certificates certifyinglower bounds of the considered global infimum even whenit is not a minimum. This is joint work with Aurelien

Greuet, Feng Guo and Lihong Zhi.

Mohab Safey El DinUPMC, Univ Paris [email protected]

MS3

Implementation of Nonsymmetric Interior-pointMethods for Linear Optimization Over Sparse Ma-trix Cones

We describe implementations of nonsymmetric interior-point methods for linear optimization over two types ofsparse matrix cones: the cone of positive semidefinite ma-trices with a given sparsity pattern, and the cone of com-pletable matrices. The implementations take advantage offast sparse matrix algorithms for evaluating the associatedlogarithmic barriers and their derivatives. We present nu-merical results of an implementation of an interior-pointalgorithm based on these techniques with applications torobust quadratic optimization problems.

Martin S. AndersenUniversity of California, Los AngelesElectrical Engineering [email protected]

Joachim DahlMOSEK [email protected]

Lieven VandenbergheUniversity of CaliforniaLos [email protected]

MS3

Semidefinite Programming Algorithm for Dis-tributed Stability Analysis

We investigate stability of uncertain large-scale intercon-nected systems using μ-analysis. The interconnections arefew. This means that the system matrix relating input tooutput signals is sparse. The μ-analysis problem can beformulated as a semidefinite programming (SDP) probleminvolving the system matrix. We will present results onhow this SDP problem can be solved efficiently in a dis-tributed fashion.

Sina Khoshfetrat PakazadDivision of Automatic ControlLinkoping [email protected]

Anders HanssonDivision of Automatic ControlLinkoping [email protected]

Anders RantzerLund [email protected]

Martin S. AndersenUniversity of California, Los AngelesElectrical Engineering [email protected]

104 OP11 Abstracts

MS3

Parallel Multilevel Computing in SDPARA forLarge-scale Semidefinite Programming

We discuss a hybrid MPI and multi-threading parallel com-putation on multi-core CPUs. It is employed in the lat-est version 7.3.1 of SDPARA (a parallel version of SDPA).SDPARA 7.3.1 adopts a new storage scheme to reduce ofmemory consumption and to derive an ideal load balanceamong processors. Numerical results show that this par-allel scheme provides an astonishing speed up on SDPs.

Kazuhiro KobayashiNational Maritime Research [email protected]

Makoto YamashitaTokyo Institute of TechnologyDept. of Mathematical and Computing [email protected]

Katsuki FujisawaDepartment of Industrial and Systems EngineeringChuo [email protected]

MS4

Enhanced Hospital Resource Management usingAnticipatory Policies in Online Dynamic Multi-objective Optimization

Evolutionary algorithms are well-suited to solve bothmulti-objective and dynamic optimization problems.Studying problems that are multi-objective and dynamicis only rather recent. An important problem difficulty (inpractice) is that decisions taken now have future conse-quences. We tackle this issue by optimizing policies thatare well-designed for the problem at hand with a multi-objective evolutionary algorithm and apply this approachto a complex, real-world optimization problem, namely themanagement of resources in a hospital.

Peter BosmanCentrum Wiskunde & Informatica (CWI)(Centre for Mathematics and Computer Science)[email protected]

MS4

Calculation of Uncertainty Information DuringCalibration

The problem of calibration of a computer simulator in-volves determining the optimal values of several tuning in-put variables that, when combined with input variablesmatching known conditions, produce output values thatmatch real observed data. At its heart is the comparisonof experimental data and simulation results. Complicat-ing this comparison is the fact that both data sets containuncertainties which must be quantified in order to makereasonable comparisons. Therefore, UQ techniques mustbe applied to identify, characterize, reduce, and, if possi-ble, eliminate uncertainties. In this talk, we will discussan approach to calibration which combines Bayesian sta-tistical models and derivative-free optimization in order tomonitor sensitivity information throughout the calibrationprocess.

Genetha Gray

Sandia National [email protected]

Herbie LeeUniversity of California, Santa CruzDept. of Applied Math and [email protected]

Katie FowlerClarkson [email protected]

MS4

Application of Optimization-Under-Uncertainty inthe Design of Pump-and-Treat Systems

Pump-and-treat systems can prevent groundwater contam-inant migration and candidate systems are typically evalu-ated via groundwater models. Such models should be cali-brated so that parameter uncertainties can be incorporatedinto subsequent simulation-based optimization. Numerouscalibration procedures have been proposed, yielding vary-ing expressions of parameter uncertainty. A series of nu-merical experiments were performed utilizing optimization-under-uncertainty to design a remedial system for ground-water contamination. Results indicate that alternative ap-proaches for parameter estimation can significantly influ-ence optimal system design.

L. Shawn Matott, Philip SheffieldUniversity of [email protected], [email protected]

MS4

Post-inference Optimization in a Multi-scaleBayesian Setting

Simulations in difficult optimization problems often dependon the solution of an inference problem. An example is thepermeability field in a well placement design problem whichis often derived from pressure or saturation measurements.Furthermore, uncertainty in the inverse solution can have asignificant impact on the optimization. Incorporating thisduring optimization is difficult and we present a method totake advantage of structure in a Bayesian inference problemduring the optimization.

Matthew Parno, Youssef M. MarzoukMassachusetts Institute of [email protected], [email protected]

MS5

Feasibility Pump Heuristics for Nonconvex MINLP

Finding feasible solutions of Mixed Integer Nonlinear Pro-gramming (MINLP) problems is crucial to the performanceof any branch-and-bound MINLP solver. We describe avariant of the Feasibility Pump heuristic, which was in-troduced for Mixed Integer Linear Programming (MILP)problems and extended to MINLP. Our implementationtakes advantage of an LP relaxation of the MINLP prob-lem that can be dynamically refined. We provide compu-tational results based on Couenne, an Open Source solverfor non-convex MINLP problems.

Pietro BelottiClemson [email protected]

OP11 Abstracts 105

Timo BertholdZuse Institute BerlinTakustr. 7 14195 [email protected]

MS5

MINOTAUR: A Solver for MINLPs

In this talk we describe MINOTAUR, a solver that we aredeveloping for general MINLPs. MINOTAUR provides aflexible framework for implementing a variety of techniquesfor relaxing, branching, cutting, searching and other meth-ods that are necessary for solving MINLPs. We describesome new techniques that we have developed and comparetheir performance to existing ones. MINOTAUR is also ca-pable of identifying certain basic problem structures thatcan be exploited effectively. We describe these methodsalso.


Ashutosh MahajanArgonne National [email protected]

Todd MunsonArgonne National LaboratoryMathematics and Computer Science [email protected]

MS5

Linear and Nonlinear Inequalities for a Nonsepara-ble Quadratic Set

We describe some integer-programming based approachesfor finding strong inequalities for the convex hull of aquadratic mixed integer nonlinear set containing two in-teger variables that are linked by linear constraints. Thisstudy is motivated by the fact that such sets appear canbe defined by a convex quadratic program, and thereforestrong inequalities for this set may help to strengthen theformulation of the original problem. Some of the inequali-ties we define for this set are linear, while others are non-linear (specifically conic). The techniques used to definestrong inequalities include not only ideas related to recentperspective reformulations of MINLPs, but also disjunctiveand lifting arguments. Initial computational tests will bepresented.

Hyemin Jeon, Jeffrey LinderothUniversity of [email protected], [email protected]

Andrew MillerInstitut de Mathematiques de [email protected]

MS5

A Computational Study on Branching and BoundTightening Techniques for MINLPs

Within the context of developing a parallel Branch-and-Bound solver for nonconvex MINLPs, we perform a com-putational investigation of branching and bound tighteningtechniques. We propose new methods that try to exploit

the large amount of CPU power available in order to reducethe size of the enumeration tree, studying their effect anddiscussing their applicability in the single-processor case.Our focus will be on bound tightening techniques. If timepermits, we will also discuss branching.

Giacomo NanniciniCarnegie Mellon UniversityTepper School of [email protected]

Pietro BelottiClemson [email protected]

Jon LeeIBM T.J. Watson Research [email protected]

Jeff LinderothUniversity of Wisconsin-MadisonDept. of Industrial and Sys. [email protected]

Francois MargotCarnegie Mellon UniversityTepper School of [email protected]

Andreas WaechterThomas J. Watson Research [email protected]

MS6

Nested Multigrid for Optimal Control of Time-periodic Parabolic PDEs

We present a nested multigrid (mg) method to solve opti-mal control problems with time-periodic parabolic PDEs.The method relies on the reduction of the first order op-timality conditions to a Fredholm integral equation of thesecond kind which is solved by the outer mg method. Inevery outer iteration a space-time mg approach of the firstkind is applied as inner mg method for the evaluation ofthe integral kernel to solve for the state and adjoint state.

Dirk AbbeloosDepartment of Computer ScienceK. U. [email protected]

Moritz [email protected]

Michael HinzeUniversitat HamburgDepartment [email protected]

Stefan VandewalleDepartment of Computer ScienceKatholieke Universiteit [email protected]

106 OP11 Abstracts

MS6

Multi-level Optimization Algorithms for PDE-constrained Problems Arising in Materials Design

Motivated by gas storage in nanoporous materials, we con-sider a novel class of optimization problems. Applicationsrequire a specified rate of charge and discharge which isfacilitated by creating channels of various widths. The ob-jective is to minimize the total volume of the channels. Thephysics changes as scale is reduced and must be correct onall scales to solve the problem. We describe extensions tothe multi-grid optimization method to solve such multi-scale problems.

Paul BoggsSandia National [email protected]

David M. GayAMPL Optimization LLCUniversity of New [email protected]

Robert M. LewisCollege of William and [email protected]

Stephen G. NashGeorge Mason UniversitySystems Engineering & Operations Research [email protected]

MS6

Nonlinear Domain Decomposition Methods for theSolution of Constrained Nonlinear ProgrammingProblems

The parallel numerical solution of realistic problems, suchas large-deformation contact between an elastic body anda rigid obstacle, gives rise to nonlinear programming prob-lems (NLPs) which will reliably be solved employing glob-alization strategies. In this talk, we will consider an ex-tension to the concept of globalization strategies, nonlin-early preconditioned globalization strategies, and focus onthe application of such strategies to the multiscale solu-tion of large-scale NLPs arising from the discretization ofconstrained PDEs.

Christian GrossUniversita’ della Svizzera ItalianaInstitute of Computational [email protected]

Rolf KrauseUniversita’ della Svizzera [email protected]

MS6

Approximation and Correction Techniques for De-sign of a Nanoporous Material

We discuss approaches to the hierarchical design of ananoporous material for energy storage. The structure andphysical nature of the material varies on different length-scales. The system can be approximated using a smallnumber of decision variables, which makes it possible toconsider algebraic approximations of the objective and con-straints in the resulting optimization problem. We discuss

such approximations, as well as techniques for aggregatinginformation from different length-scales for the purposes ofoptimization.

Robert M. LewisCollege of William and [email protected]

MS7

Infeasibility Detection in Nonlinear Programming

We address the deficiencies of current nonlinear optimiza-tion software with respect to infeasibility detection. Inparticular, it is suggested in this talk that algorithms bereworked and reanalyzed so that, if given an infeasibleproblem, useful information is returned to the user effi-ciently. We also propose our own approaches for sequen-tial quadratic optimization and interior-point methods thatprovide the same convergence guarantees as contemporarymethods, but also provide fast local convergence guaran-tees for infeasible problems.

Frank E. Curtis, Hao WangIndustrial and Systems EngineeringLehigh [email protected], [email protected]

MS7

Active Set Strategies for the Gradient ProjectionAlgorithm

When solving a nonlinear programming problem using thegradient projection method, we often need to project avector into the linearized constraints. Active set strategiesfor solving the projection problem are examined, includingthe dual active set algorithm.

William HagerUniversity of [email protected]

MS7

A Robust Algorithm for Semidefinite Program-ming

Current successful methods for solving semidefinite pro-grams, SDP, use symmetrization and block eliminationsteps that create ill-conditioning in the Newton equations.We derive and test a backwards stable primal-dual interior-point method for SDP that avoids the ill-conditioning. Ouralgorithm is based on a Gauss-Newton approach that al-lows for a preconditioned (matrix-free) iterative methodfor finding the search direction at each iteration.

Henry WolkowiczUniversity of WaterlooDepartment of Combinatorics and [email protected]

Xuan Vinh DoanC&O DepartmentUniversity of [email protected]

Serge KrukDepartment of Mathematics and StatisticsOakland University, Rochester, [email protected]

OP11 Abstracts 107

MS7

A Trust Region Algorithm for Inequality Con-strained Optimization with a New Scaling Tech-nique

In this paper, we propose a trust region algorithm for in-equality constrained optimization with a new scaling tech-nique. The scaling is derived by considering the specialcase of bound constraints, where the scaling matrix de-pends on the gradients of the objective function and thedistances to the bounds. Global convergence results of thealgorithm are presented.

Xiao WangInst of Comp Math & Sci/Eng. AMSSChinese Academy of [email protected]

Ya-Xiang YuanChinese Academy of SciencesInst of Comp Math & Sci/Eng, [email protected]

MS8

Efficient Aerodynamic Design

We present our methods for aircraft aerodynamic shape op-timization based on Computational Fluid Dynamics. Theexamples of applications are total drag minimization atcruise flight conditions, which involves resolving the prop-agation of disturbances in the boundary layer, and lift max-imization at landing and take-off, which requires solutionsof the Reynolds Averaged Navier-Stokes equations. Wealso present our investigations in static aeroelastic opti-mization based on CFD.

Olivier G. AmoignonFOI-Swedish Defence Research [email protected]

Ardeshir Hanifi, Jan Pralits, Daniel Skoogh, FredrikBerefelt, Lars Tysell, Adam Jirasek, Mattias [email protected], [email protected],[email protected], [email protected],[email protected], [email protected],[email protected]

MS8

An Adaptive One-Shot Approach for AerodynamicShape Optimization

We focus on so-called one-shot methods and their ap-plications to aerodynamic shape optimization, where thegoverning equations are the Navier-Stokes or Reynolds-averaged Navier-Stokes (RANS) equations. We constrainthe one-shot strategy to problems, where steady-state solu-tions are achieved by pseudo-time stepping schemes. Theone-shot optimization strategy pursues optimality simul-taneously with the goals of primal and adjoint feasibility.To exploit the domain specific experience and expertise in-vested in the simulation tools, we propose to extend themin an automated fashion by the use of automatic differentia-tion (AD). First they are augmented with an adjoint solverto obtain (reduced) derivatives and then this sensitivity in-formation is immediately used to determine optimizationcorrections. Finally, we discuss how to use the adjoint so-lutions also for goal-oriented error estimation and how tomake use of the resulting error sensor for mesh adaptation

and its integration into the presented one-shot procedure.

Nicolas R. GaugerDepartment of Mathematics and CCESRWTH Aachen [email protected]

MS8

Avoiding Mesh Deformations in Boundary ShapeOptimization

We propose an approach to boundary shape optimizationin which the geometry is represented through varying coef-ficients in the governing equation. Our method constructsraster representations of the geometries, which circumventsthe need for re-meshing and enables flexible choices of ad-missible designs. The method has been assessed on anacoustic optimization problem, using a shape parameteri-zation that is difficult to employ with traditional methods,for which it generated visually smooth devices with favor-able acoustic properties.

Fotios KasolisDepartment of Computing ScienceUmea University, [email protected]

Eddie WadbroDepartment of Computing ScienceUmea [email protected]

Martin BerggrenDepartment of Computing Science, Umea [email protected]

MS8

Aerodynamic Design based on Shape Calculus

Shape optimization based on the Hadamard form of theshape derivative is considered. The Hadamard form pro-vides an analytically exact surface formulation of the gradi-ent, allowing shape optimization without the need to com-pute so called mesh sensitivities. Thus, shape optimizationbased on a first optimize then discretize fashion is enabled,where e.g. all mesh surface nodes can be used as design un-knowns with next to no additional costs. Furthermore, ap-proximations to shape Hessians are considered, thereby cre-ating a shape one-shot optimization method. The talk con-culdes with the optimization of a blended wing-body air-craft using 113,956 surface nodes as the shape unknowns.

Stephan SchmidtUniversity of [email protected]

MS9

4D Imaging using Optimal Transport and SparsityConcepts

We present models and efficient algorithms for 4D recon-struction in biomedical imaging using optimal transportand sparsity concepts. Standard reconstruction methodsdo not incorporate time dependent information or kinetics.This can lead to deficient accuracy particularly at objectboundaries, e.g. at cardiac walls. We discuss constraintoptimization models combining reconstruction techniques

108 OP11 Abstracts

known from inverse problems, spatio-temporal regulariza-tion and mass conservation. The numerical realization isbased on multigrid preconditioned Newton-SQP with fil-tered line-search and efficient operator splitting techniqueswith parallelization. Dynamic large-scale biomedical dataillustrate the performance of our methods.

Christoph BruneInstitute for Computational and Applied MathematicsUniversity of Muenster, [email protected]

Martin BurgerInstitute for Numerical and Applied MathematicsUniversity of [email protected]

Eldad HaberDepartment of MathematicsThe University of British [email protected]

MS9

Numerical Optimization for Constrained ImageRegistration with Application to Medical Imaging

Image registration is a technique aimed at establishingmeaningful correspondences between image voxels from dif-ferent perspectives. It is an essential tool for various ap-plications in medicine, geosciences, and other disciplines.However, obtaining plausible deformations is a complextask as often transformations are required to be locallyinvertible or even more challenging, are required to boundvolume changes within a reasonable range. In this work,solutions to the registration problem were obtained by di-rectly imposition of a volume constraint upon each voxelin a discretized domain. This study focuses on the devel-opment of an efficient and robust numerical algorithm andin particular, the application of an augmented Lagrangianmethod with a multigrid as preconditioner. We demon-strate that this combination yields an almost optimal solverfor the problem.

Raya HoreshInstitute of Mathematics and its ApplicationsUniversity of [email protected]


Jan ModersitzkiUniversity of LubeckInstitute of Mathematics and Image [email protected]

MS9

Optimal Control of the Bidomain Equations

Well-posedness of the bidomain equations is investigatedfor several well-established ionic current models. Optimalcontrol problems are formulated to influence the extra andintracellular potentials by means of extracellular appliedcurrent. Optimality conditions are derives rigorously. Nu-merical examples illustrate, for the two dimensional case,the feasibility of dampening excitation waves and control-

ling reentry phenomena.

Karl KunischKarl-Franzens University GrazInstitute of Mathematics and Scientific [email protected]

Nagaiah Chamakuri, Marcus WagnerKarl-Franzens University [email protected],[email protected]

MS9

Large Scale Optimization Problems in MedicalImaging

This talk presents a brief introduction to image registrationand introduces the FAIR (Flexible Algorithms for ImageRegistration) package for a numerical solution using MAT-LAB. Moreover, a new component which enables mass pre-serving registration is discussed. The mass preserving reg-istration is based on a new and thorough discretization ofthe determinant of the Jacabian and the co-factor matrix.Numerical results related to fast magnetic resonance imag-ing sequences are presented.

Jan ModersitzkiUniversity of LubeckInstitute of Mathematics and Image [email protected]

Lars RuthottoInstitute of Mathematics and Image [email protected]

MS10

Conservation Laws Coupled with Ordinary Differ-ential Equations

This presentation describes some recent results concerningthe basic well posedness theory of systems consisting ofconservation laws coupled with ordinary differential equa-tions. Several examples will be considered in more detailand numerical result will be presented.

Rinaldo M. ColomboUniversity of BresciaDepartment of [email protected]

MS10

Feedback Stabilization for the Gas Flow in Net-works

The control of the gas flow in pipe networks plays an im-portant role for the supply with natural gas. The gas flowthrough pipelines can be modeled by the isothermal Eu-ler equations with friction, which are a hyperbolic 2x2-PDE-system of balance laws. We present recent resultson the boundary feedback stabilization of the isothermalEuler equations locally around a given stationary state.The stabilization methods are based upon transformationto Riemann invariants and upon Lyapunov functions. Thefeedback laws guarantee an exponential decay of the Lya-punov functions with time.

Markus DickUniversitat Erlangen-Nurnberg

OP11 Abstracts 109

Dept. of [email protected]

MS10

On Control and Controllability of Systems of Non-linear Conservation Laws

We give an overview on optimal control and controllabil-ity for one–dimensional hyperbolic systems. We present ashort summary of theoretical as well as numerical results.Applications towards network flows and controllability re-sults on those are given.

Michael HertyRWTH Aachen UniverstiyDepartment of [email protected]

MS10

Numerical Approximation of Optimal ControlProblems for Discontinuous Solutions of Hyper-bolic Conservation Laws

We analyse the convergence of discrete approximations tooptimal control problems for discontinuous solutions ofhyperbolic conservation laws. Building on a sensitivityand adjoint calculus for the optimal control problem weshow that an appropriate discretization by finite differenceschemes with sufficient numerical viscosity at shock dis-continuities leads to convergent approximations of the lin-earized and the adjoint equation and thus to convergentgradient approximations of the cost functional. Hence, ef-ficient optimization methods are applicable. We presentnumerical results.


MS11

Set-Valued Optimization Revisited: From MinimalPoints to Lattice Solutions

Motivated by duality issues, set-valued optimization prob-lems have been studied since the 1980ies. Later, Tanakaet al. initiated solution concepts based on set relations.Recently, it has been shown that set-valued optimization(only) admits a complete (duality) theory if lattice exten-sions both of image and pre-image space are used. Thistheory matches the needs of applications in finance: opti-mization problems for set-valued risk measures in marketswith transaction costs. The talk will be a guided tourthrough these subjects.

Andreas H. HamelYeshiva UniversityDepartment of Mathematical [email protected]

MS11

About Set-valued Optimization via the Set Scheme

The goal of this talk is to explore solution concepts inset-valued optimization and to clarify some links betweenthem. Exactly, we study some criteria of solution asso-ciated to a set-valued optimization problem and we giveoptimality conditions by revising several existing results in

the literature.

Elvira HernandezDepartamento de Matematica AplicadaUNED [email protected]

Miguel SamaUniversidad Nacional de Educacion a [email protected]

Luis [email protected]

MS11

Fenchel-Rockafellar Duality for Set-valued Prob-lems via Scalarization

New Fenchel-Rockafellar type duality results for set-valuedoptimization problems are proven. The image space is acomplete lattice of subsets of a preordered locally convexspace. The proof consists of characterizing set-valued func-tions by families of extended real-valued ones and apply-ing the scalar result. As corollaries, calculus rules for set-valued conjugates are shown. Applications to vector op-timization problems are given by introducing a set-valueddual.

Carola SchrageInstitute for MathematicsMartin-Luther-University [email protected]

Andreas H. HamelYeshiva UniversityDepartment of Mathematical [email protected]

MS11

Lagrange Necessary Conditions for Pareto Mini-mizers in Asplund Spaces and Applications

In this talk, new necessary conditions for Pareto mini-mal points of sets and Pareto minimizers of constrainedmultiobjective optimization problems are established with-out the sequentially normal compactness property and theasymptotical compactness condition imposed on closed andconvex ordering cones. Our approach is based on a ver-sion of a separation theorem for nonconvex sets and thesubdifferentials of vector-valued and set-valued mappings.Furthermore, applications in mathematical finance and ap-proximation theory are discussed.

Christiane TammerFaculty of Sciences III, Institute of MathematicsUniversity of [email protected]

Bao Q. TruongMathematics and Computer Science. DepartmentNorthern Michigan [email protected]

MS11

Extended Pareto Optimality in Multiobjective

110 OP11 Abstracts

Problems

This talk presents new developments on necessary condi-tions for minimal points of sets and their applications toderiving refined necessary optimality conditions in generalmodels of set-valued optimization with geometric, func-tional, and operator constraints in finite and infinite di-mensions. The results obtained address the new notionsof extended Pareto optimality with preference relationsgenerated by ordering sets satisfying the local asymptoticclosedness property instead of that generated by convexand closed cones. In this way we unify and extend mostof the known notions of efficiency/optimality in multiob-jective models and establish optimality conditions that arenew even in standard settings. Our approach is based onadvanced tools of variational analysis and generalized dif-ferentiation.

Bao Q. TruongMathematics and Computer Science. DepartmentNorthern Michigan [email protected]

Boris MordukhovichWayne State UniversityDepartment of [email protected]

MS12

On Calmness Conditions in Convex Bilevel Pro-gramming

We compare two well-introduced calmness conditions inthe context of convex bilevel programming, namely partialcalmness related to the value function approach and calm-ness of the solution set to the lower level problem underlinear perturbations of the lower level objective. Both con-cepts allow to derive first order necessary optimality condi-tions. They differ, however, in their assumptions and in theresulting optimality conditions. We illustrate by theoreti-cal results as well as by the example of a dicretized obstaclecontrol problem that partial calmness is too restrictive ingeneral.

Rene HenrionWeierstrass InstituteBerlin, [email protected]

Thomas M. SurowiecDepartment of MathematicsHumboldt University of [email protected]

MS12

Handling Set Constraints in Variational Problemslike Usual Inequalities

In many optimization and variational problems, abstractset-constraints of the type h(x) ∈ C, C polyhedral, ap-pear. Such set constraints are often handled separately inits algebraic form when deriving stability (and solvability)conditions, since standard constraint qualifications may failto hold. We show how such problems can be rewritten intraditional inequality and equation form in such a way thatresults on stability of solutions and feasible points for therelated classical models can be directly applied.

Diethard Klatte

University of [email protected]

Bernd KummerHumboldt-University of [email protected]

MS12

Introduction to Mathematical Programs with ConeComplementarity Constraints

Optimization problems involving symmetric positivesemidefinite matrix variables,i.e., Semidefinite programs(SDPs), are well studied in engineering control and struc-tural mechanics. Mathematical programs with semidefi-nite complementarity constraints are nonconvex optimiza-tion problems arising, e.g., as inverse problems when theforward model is an SDP. After penalizing the complemen-tarity/orthogonality constraint,a nonconvex problem withboth matrix and vector variables and constraints remains.Stationarity conditions are analyzed and the penalty for-mulation is solved for an application from structural opti-mization.

Daniel RalphUniversity of CambridgeDept. of Engineering & Judge Institute of [email protected]

Michal KocvaraSchool of MathematicsUniversity of [email protected]

MS12

On the Derivation of Optimality Conditions for El-liptic MPECs via Variational Analysis

An elliptic MPEC is any mathematical program whose fea-sible set is governed by an elliptic variational inequality.After demonstrating new results concerning the contingentderivative of the solution mapping associated with the vari-ational inequality, we derive an upper approximation ofthe Frechet normal cone of the feasible set. This leads tooptimality conditions resembling S-stationarity conditions.The strength of the results are then demonstrated by con-sidering a model from the theory of elastoplasticity.

Thomas M. SurowiecDepartment of MathematicsHumboldt University of [email protected]

MS13

Semidefinite Programming and Occupation Mea-sures for Impulsive Control of Dynamical Systems

The problem of dynamical systems control can be ap-proached constructively via occupation measures charac-terised by their moments satisfying semidefinite program-ming constraints. This allows for a genuine primal ap-proach focusing on systems trajectories, in contrast withmore classical dual approaches based on Lyapunov or simi-lar energy functionals satisfying Hamilton-Jacobi-Bellmanpartial differential equations. We survey recent achieve-ments in the area, with a focus on the design of impulsivecontrol laws with application in satellite orbital transferproblems. Joint work with Denis Arzelier, Mathieu Claeys

OP11 Abstracts 111

and Jean-Bernard Lasserre.

Didier HenrionLAAS-CNRS, University of Toulouse, & Faculty ofElectrical Engineering, Czech Technical [email protected]

MS13

Algebraic Certificates for Linear Matrix Inequali-ties and Semidefinite Programming

Given linear matrix inequalities (LMIs) L1 and L2 it isnatural to ask:

1. when does one dominate the other, that is, doesL1(X) 0 imply L2(X) 0?

2. when are they mutually dominant, that is, when dothey have the same solution set?

In this talk we describe a natural relaxation of an LMI,based on substituting matrices for the variables xj . Withthis relaxation, the domination questions (1) and (2) haveelegant answers. Assume there is an X such that L1(X)and L2(X) are both positive definite, and suppose the pos-itivity domain of L1 For our “matrix variable’ relaxationa positive answer to (1) is equivalent to the existence ofmatrices Vj such that

L2(x) = V ∗1 L1(x)V1 + · · · + V ∗

μ L1(x)Vμ. (1)

As for (2), L1 and L2 are mutually dominant if and only if,up to certain redundancies, L1 and L2 are unitarily equiva-lent. Particular emphasis will be given to the case of emptyLMI sets

{X | L(X) 0}.We shall explain how to derive a polynomial sos version ofthe Farkas lemma for linear programming thus giving riseto a polynomial size infeasibilty certificate for semidefiniteprograms (SDP). The talk is based on joint works withM. Schweighofer, and J.W. Helton and S. McCullough; seee.g. http://arxiv.org/abs/1003.0908

Igor KlepUniversity of California, San [email protected]

MS13

Error Bounds for Sums of Squares Relaxations ofSome Polynomial Optimization Problems

We consider semidefinite programming relaxations forpolynomial optimization problems based on sums ofsquares of polynomials and the dual relaxations based onmoment matrices. In particular, we give new error boundsfor optimization over the hypercube for the hierarchy of re-laxations corresponding to Schmudgen’s Positivstellensatz.These bounds are explicit and sharpen an earlier result ofSchweighofer (2004). This is based on joint work with E. deKlerk. We also discuss recent bounds of Karlin, Mathieuand Nguyen (2011) for the case of a linear objective anda unique linear constraint (corresponding to the knapsackproblem) and show that they extend to a block-diagonalversion of Lasserre’s hierarchy.

Monique LaurentTilburg UniversityCWI, [email protected]

Etienne Klerk, de

Faculty of Economic SciencesTilburg [email protected]

MS13

Polya’s Theorem and Optimization

Let R[X] := R[X1, . . . , Xn]. Polya’s Theorem says that ifa form (homogeneous polynomial) p ∈ R[X] is positive onthe standard n-simplex Δn, then for sufficiently large Nall the coefficients of (X1 + · · · + Xn)Np are positive. In2001, Powers and Reznick gave a bound on the N needed,in terms of the degree of p, the coefficients, and minimumof p on . This quantitative Polya’s Theorem has many ap-plications, in both pure and applied mathematics. For ex-ample, it is an ingredient in the degree bound for Putinar’sPositivstellensatz given by J. Nie and M. Schweighofer in2007. This degree bound gives information about the con-vergence rate of Lasserre’s procedure for optimizaiton ofa polynomial subject to polynomial constraints. In jointwork with M. Castle and B. Reznick, we extend the quanti-tative Polya’s Theorem to forms which are allowed to havezeros on Δn. We give a complete characterization of formsfor which the conclusion of Polya’s Theorem holds (with“positive on Δn” relaxed to “nonnegative on Δn”), and abound on the N . We discuss these results and connectionswith optimization using Lasserre’s method.

Victoria PowersEmory [email protected]

MS14

An Introduction to a Class of Matrix Cone Pro-gramming

In this talk, we introduce a class of matrix cone program-ming (MCP), which consists of linear conic programmingproblems whose conic constraints involve the epigraphs ofl1, l∞, spectral or nuclear matrix norms. We study severalimportant properties, including its closed form solution,calm Bouligand-differentiability and strong semismooth-ness, of the metric projection operator over these matrixcones. These properties make it possible to design some ef-ficient algorithms such as augmented Lagrangian methods,to solve MCP problems.

Chao DingNational University of [email protected]



MS14

Iteration-Complexity of Block-Decomposition Al-gorithms and the Alternating Minimization Aug-mented Lagrangian Method

In this talk, we discuss the complexity of block-decomposition methods for solving monotone inclusion

112 OP11 Abstracts

problems consisting of the sum of a continuous monotonemap and a point-to-set maximal monotone operator with aseparable two-block structure. As a consequence, we derivecomplexity results for alternating minimization augmentedLagragian methods for for solving block-structured convexoptimization problems. Moreover, we also apply our re-sults to derive new methods and corresponding complexityresults for the monotone inclusion problem consisting ofthe sum of two maximal monotone operators.

Renato C. MonteiroGeorgia Institute of TechnologySchool of [email protected]

Benar SvaiterIMPARio de Janeiro, [email protected]

MS14

An Inexact Interior Point Method for L1-regularized Sparse Covariance Selection

Sparse covariance selection (CSC) problems can be for-mulated as log-determinant optimization problems withlarge number of linear constraints. We propose a cus-tomized inexact interior-point algorithm for solving suchlarge scale problems. At each iteration, we solve the largeand ill-conditioned linear system of equations by an it-erative solver using highly effective preconditioners con-structed based on the special problem structures. Nu-merical experiments on synthetic and real CSC problemsshow that our algorithm can outperform other existing al-gorithms.


Lu LiANZ [email protected]

MS14

A Proximal Point Algorithm for Log-DeterminantOptimization with Group Lasso Regularization

We propose a practical proximal point algorithm for solv-ing large scale log-determinant optimization problem withgroup Lasso regularization and linear equality constraints.At each iteration, as it is difficult to update the primalvariables directly, we solve the dual problem by a Newton-CG method, and update the primal variables by an explicitformula based on the computed dual variables. We presentnumerical results to demonstrate that the proposed algo-rithm is efficient, especially when high accuracy is required.

Junfeng YangNanjing [email protected]


Kim-Chuan Toh

National University of SingaporeDepartment of Mathematics and Singapore-MIT [email protected]

MS15

Optimizing over the Complement of Ellipsoids

We describe continuing work related to the optimization ofconvex functions over the complement of a union of ellip-soids. This arises in several practical nonconvex optimiza-tion problems, and is related to several fundamental prob-lem areas in optimization. Joint work with Alex Michalkaand Mustafa Tural.

Daniel BienstockColumbia University IEOR and APAM DepartmentsIEOR [email protected]

MS15

Pooling Problems with Binary Variables

The pooling problem consists of finding the optimal quan-tity of final products to obtain by blending different compo-sitions of raw materials in pools. We study a generalizationof the problem where binary variables are used to modelfixed costs associated with using a raw material in a pool.We derive four classes of strong valid inequalities, that canbe separated in polynomial time, and dominate classic flowcover inequalities. Successful computational results are re-ported.

Claudia D’AmbrosioUniversity of [email protected]


James LuedtkeUniversity of Wisconsin-MadisonDepartment of Industrial and Systems [email protected]

MS15

Computationally Effective Disjunctive Cuts forConvex Mixed Integer Nonlinear Programs

We discuss computationally effective methods for generat-ing disjunctive inequalities for convex mixed-integer non-linear programs (MINLPs). Computational results indi-cate that disjunctive inequalities have the potential toclose a significant portion of the integrality gap for convexMINLPs and to be as effective for solving convex MINLPsas they have been for solving mixed-integer linear pro-grams.

Mustafa KilincUniversity of Wisconsin-MadisonDept. of Industrial and Sys. [email protected]

Jeff LinderothUniversity of Wisconsin-MadisonDept. of Industrial and Sys. Eng

OP11 Abstracts 113

[email protected]

Jim LuedtkeUniversity of Wisconsin-MadisonDept. of Industrial and Sys. [email protected]

MS15

Lifted Inequalities for Mixed Integer NonlinearSets with Special Structure

Lifting is the process of converting a seed inequality validfor a restriction of the set to the unrestricted set. We applylifting to specially-structured nonlinear sets. For mixed-binary bilinear knapsacks, we derive inequalities that arenot easily obtained using IP techniques. For mixed-binarybilinear covers, we obtain facet-defining inequalities thatgeneralize well-known inequalities for certain flow mod-els. Finally, we derive valid nonlinear inequalities for dis-junctive sets by projecting families of parameterized linearlifted inequalities.

Mohit TawarmalaniPurdue [email protected]

Jean-Philippe RichardDepartment of Industrial and Systems EngineeringUniversity of [email protected]

Kwanghun ChungCenter for Operations Research and [email protected]

MS16

The Lifted Newton Method for Nonlinear Opti-mization

The lifted Newton method is designed for the solution ofnonlinear optimization problems that have objective andconstraint functions with intermediate variables. Introduc-ing these as additional degrees of freedom into the originalproblem offers more freedom for initialization and often,faster contraction rates are observed. An algorithmic trickallows us to perform each lifted Newton iteration at al-most no additional computational cost compared to a non-lifted Newton iteration. We discuss under which conditionsfaster local quadratic convergence for lifted iterations canbe expected, and demonstrate the speedup due to the liftedNewton method at a large PDE parameter estimation ex-ample. Part of the material was published in [Albersmeyerand Diehl, The Lifted Newton Method and Its Applicationin Optimization. SIAM Journal on Optimization (2010)20:3,1655-1684].


Jan Albersmeyerpreviously at IWR, Uni [email protected]

MS16

Domain Decomposition Methods for Structural

Optimization

We investigate two approaches to the solution of topologyoptimization problems using decomposition of the compu-tational domain. The first approach is based on a twostage algorithm; a block Gauss-Seidel algorithm is com-bined with a first order method guaranteeing convergence.The second approach uses the semidefinite programmingformulation of the problem. We replace the original largematrix constraint by several smaller constraints. This leadsto a significant improvement in efficiency.

Michal KocvaraSchool of MathematicsUniversity of [email protected]

Masakazu KojimaTokyo Institute of [email protected]

James TurnerSchool of MathematicsUniversity of Birmingham, [email protected]

MS16

Inexact Solution of NLP Subproblems in MINLP

We investigated how the outer approximation method andthe generalized Benders decomposition method are affectedwhen the NLP subproblems are solved inexactly. We showthat the cuts in the master problems can be changed to in-corporate the inexact residuals, still rendering equivalenceand finiteness in the limit case. Some numerical resultswill be presented to illustrate the behavior of the methodsunder NLP subproblem inexactness.

Luis N. Vicente, Min LiUniversity of [email protected], [email protected]

MS16

Fast NLP Solvers for MINLP

Branch-and-bound is the underlying framework for all effi-cient mixed-integer optimization solvers. In the linear case(MILP), significant speed improvements have been madeusing strong-branching and diving techniques, because LPsolvers can handle problem changes consisting of changingjust one bound very effectively. In this talk, we explorewhether similar improvements can be made in the nonlin-ear (MINLP) context.

Andreas WaechterThomas J. Watson Research [email protected]

MS17

A Linearized Model for Dynamic Positron Emis-sion Tomography

Dynamic Positron Emission Tomography allows monitor-ing physiological processes within the body that can be de-scribed by kinetic parameters. However, recovery of theseparameters often requires the solution of complex and non-linear operator equations. A variational framework is intro-duced that allows to promote sparsity of minimizers with

114 OP11 Abstracts

respect to a temporal exponential basis.

Martin BenningInstitute for Computational and Applied MathematicsUniversity of [email protected]

MS17

Exact Relaxation to Bounded Variation Problems

In this talk, we consider a class of problems given by theconstrained minimization problems of the form

min(u,v)∈BV (Ω;{0,1})×V

F (v) +

∫Ω

G(v)u dx + TV (u), (2)

where F : V → R is a (sequentially)weakly lower semicon-tinuous functional bounded below and G : V → L√

(⊗) is astrongle continuous nonlinear operator for some p > 1. Themodel covers a lot of applications, such as the total varia-tion (ROF) model for binary image restoration, Mumford-Shah model for image segmentation, minimal compliancein topology optimization, etc. In order to solve these bi-nary constrained problems, we introduce the exact relax-ation of (1) and give an efficient algorithm based on theFenchel dual technique. Moreover, we show that the min-imizers of (1) are able to be obtained by taking level setsof minimizers of the relaxation.

Yiqiu DongInstitute of Biomathematics and BiometryHelmholtz Zentrum [email protected]


Martin BurgerInstitute for Numerical and Applied MathematicsUniversity of [email protected]

MS17

Dynamic PET Reconstruction using Parallel ProX-imal Algorithm

We propose to extend a recent convex optimization ap-proach based on the Parallel ProXimal Algorithm to im-prove the estimation at the voxel level in dynamic PositronEmission Tomography (PET) imaging. The criterion to beminimized is composed with a Kullback-Leibler divergenceas a data fidelity term, an hybrid regularization (definedas a sum of a total variation and a sparsity measure), anda positivity constraint. The total variation is applied toeach temporal frame and a wavelet regularization is con-sidered for the space+time data. This allows us to smooththe wavelet artifacts introduced when the wavelet regular-ization is used alone. The proposed algorithm is evaluatedon simulated and real dynamic fluorodeoxyglucose (FDG)brain data.

Caroline ChauxUniversite [email protected]

Claude ComtatSHFJ, [email protected]

Jean-Christophe Pesquet, Nelly PustelnikLIGMUniversite [email protected],[email protected]

MS17

Image Restoration in the Presence of Non-additiveNoise

We are concerned with the restoration of (blurred) imagescorrupted by multiplicative or Poisson noise. On the onehand, we propose alternating direction methods of multi-pliers for minimizing an I-divergence/TV functional whichis related to both multiplicative and Poisson noise. On theother hand, we suggest novel nonlocal filters for removingmultiplicative noise. To this end, a suitable similarity mea-sure has to be found for defining the weights occurring inthese filters in dependence on the noise statistics.

Gabriele SteidlInstitute of Mathematics und Computer ScienceUniversitaet Mannheim, [email protected]

Tanja TeuberUniversity of Mannheim, GermanyDept. of Mathematics and Computer [email protected]

MS18

Optimal Treatment Strategies Determined by Ki-netic Equations

Using a Boltzmann transport model, we consider the ques-tion of optimal treatment strategies in radiation therapy.We derive optimality conditions for an optimal controlproblem with space-dependent constraints on the size ofthe dose and present numerical results.

Richard C. BarnardRWTH Aachen UniversityCenter of Computational Engineering [email protected]

MS18

Title Not Available at Time of Publication

TBA.

Gunter LeugeringUniversity Erlangen-NurembergInstitute of Applied [email protected]

MS18

Relaxation Schemes and Optimal Control

Relaxation schemes are well-known and easy to implementdiscretization schemes for systems of conservation or bal-ance laws. Hereby, the original (nonlinear) system of bal-ance laws is replaced by a linear system of double size,called the relaxation system. Using asymptotic analysisit can be shown that the relaxation system is well-posedif the new system matrix satisfies the so-called subchar-acteristic condition. Under this assumption a solution tothe relaxation system is known to converge to a solutionof the original system. Furthermore, using IMEX-schemes

OP11 Abstracts 115

for the time integration of the numerical scheme, it canbe shown that the discretized relaxation system convergesto a discretization of the limit equations. To provide con-sistent schemes for optimal control, we derive conditionssuch that the discrete adjoint of the relaxation system isa valid discretization of the continuous adjoint relaxationsystem in the context of smooth solutions. Furthermore,we prove that the discretization of the adjoint relaxationsystem converges to a discretization of the adjoint limitequation. This discretization then turns out to be the ad-joint of the discretized limit equation.

Veronika SchleperUniversity of StuttgartInstitute of applied Analysis and Numerical [email protected]

MS18

H1-controllability of Nonlinear Conservation Laws

We present a relaxation scheme to the optimal control ofnonlinear hyperbolic systems, in particular the control ofEuler flows in gas dynamics. The relaxation approximationunder consideration has a linear transport part combinedwith a stiff source term. We discuss how the relaxationscheme can be applied to controllability problems involvingnonlinear hyperbolic equations. We present some numeri-cal results.

Sonja SteffensenRWTH Aachen UniversityDept. of [email protected]

MS19

Derivative Free Optimization Method with NonLinear Constraints: Some Industrial Applications

Derivative free optimization takes place in various applica-tion fields and often requires dedicated techniques to limitthe number of evaluations of the usually time consumingsimulator. We propose the Sequential Quadratic Approx-imation method (SQA) based on a trust region methodwith quadratic interpolation models. Its efficiency is illus-trated on two industrial applications: an inverse problemfor reservoir characterization which requires an adaptedimplementation for least-square problems and an enginecalibration problem with derivative free constraints.

Delphine SinoquetIFP Energies [email protected]

Delbos Frederic, Langouet [email protected], [email protected]

MS19

Challenges in Derivative-free Optimization

Derivative-free optimization made substantial progresssince the times of the Nelder-Mead simplex method. Butseveral important challenges remain. In particular, there isa need for improvements in at least three areas where cur-rent methods frequently perform poorly: – the large-scalecase (50 or more variables), – the noisy case (uncertaintiesof 10% or more), – the constrained case (tight black boxconstraints). This talk reviews some of the better tech-

niques, including new approaches.

Arnold NeumaierUniversity of ViennaDepartment of [email protected]

MS19

An Active Set Trust-region Method for Derivative-free Nonlinear Bound-constrained Optimization

We consider an implementation of a recursive model-based active-set trust-region method for solving bound-constrained nonlinear non-convex optimization problemswithout derivatives using the technique of self-correctinggeometry proposed in [Scheinberg and Toint, 2009]. Con-sidering an active-set method in model-based optimizationcreates the opportunity of saving a substantial amount offunction evaluations. It allows to maintain much smallerinterpolation sets while proceeding optimization in lowerdimensional subspaces. The resulting algorithm is shownto be numerically competitive.

Anke TroeltzschCERFACSToulouse, [email protected]

Philippe L. TointUniversity of [email protected]

Serge GrattonENSEEIHT, Toulouse, [email protected]

MS20

Computational Experiencewith Copositive Programming-Based Approxima-tions of the Stability Number

We present recent advances in the approximate computa-tion of the stability number of a graph using the doublynonnegative relaxation introduced by Lovasz, McEliece,Rodemich, Rumsey, and Schrijver. Two possible improve-ments to handle its quadratic number of constraints arediscussed. First, we consider reducing the size of theoriginal relaxation by a partial aggregation of its equal-ity constraints. Second, we relax the doubly nonnega-tive relaxation to a semidefinite relaxation and discussa new cutting-plane method to handle the nonnegativityconstraints more efficiently. The approach is based on anew interior-point algorithm that selects relevant sets ofinequalities dynamically while exploiting the capability towarm start problems after updates without the need torestart or to modify previous iterates. We present com-putational results that quantify the computational benefitfrom each of these two techniques.

Miguel F. AnjosMathematics and Industrial Engineering & GERAD

Ecole Polytechnique de [email protected]

Alexander EngauUniversity of Colorado, Denver, [email protected]

116 OP11 Abstracts

Immanuel BomzeUniversity of [email protected]

MS20

Second Order Motivated Scaling Approaches forthe Spectral Bundle Method

The spectral bundle method is a nonsmooth first ordersolver for semidefinite optimization over large sparse matri-ces. Oustry outlined how to combine first order approacheswith the second order approach of Overton and Womer-sly. We report on work in progress towards using secondorder models in a large scale setting for practical scalingvariants within the spectral bundle package “ConicBundle”and present first numerical results.


Michael L. OvertonNew York UniversityCourant Instit. of Math. [email protected]

Franz RendlAlpen-Adria Universitaet [email protected]

MS20

Semidefinite Relaxations of Ordering Problems

Ordering problems assign weights to each ordering and askto find an ordering of maximum weight. The linear order-ing problem is wells tudied, with exact solution methodsbased on polyhedral relaxations. The quadratic orderingproblem does not seem to have attracted similar attention.We present a systematic investigation of semidefinite opti-mization based relaxations for the quadratic ordering prob-lem, extending and improving existing approaches. Weshow the efficiency of our relaxations by providing compu-tational experience on a variety of problem classes.

Philipp Hungerlaender, Franz RendlAlpen-Adria Universitaet [email protected], [email protected]

MS20

A Semidefinite Relaxation for Sparse Max-CutProblems

We investigate semidefinite relaxations of the Max-Cutproblem, which are formulated in terms of the edges of thegraph, thereby exploiting the (potential) sparsity of theproblem. We show how this is related to higher order lift-ings of Anjos and Wolkowicz and Lasserre. Contrary to thebasic semidefinite relaxation, which is based on the nodes ofthe graph, the present formulation leads to a model whichis significantly more difficult to solve. To solve the result-ing SDP we developed an algorithm where we factorizethe matrix in the dual SDP and apply an augmented La-grangian algorithm to the resulting minimization problem.We present computational results that indicate that thismodel is manageable for sparse graphs on a few hundred

nodes and yields very tight bounds.

Veronica PiccialliUniversita degli Studi di Roma Tor [email protected]

Franz RendlUniversitat KlagenfurtInstitut fur [email protected]

Angelika Wiegele

Alpen-Adria-Universit{”a}t KlagenfurtInstitut f. [email protected]

MS21

Minty Variational Principle for Set-valued Varia-tional Inequalities

It is well known that a solution of a Minty scalar variationalinequality of differential type is a solution of the relatedoptimization problem, under lower semicontinuity assump-tion. This relation is known as ”Minty variational princi-ple”. In this presentation we study this principle in thevector case for an arbitrary ordering cone and a non differ-entiable objective function. Further, we extend the Mintyvariational principle to set-valued variational inequalities.

Giovanni CrespiUniversite de la Vallee d’[email protected]

Ivan Ginchev, Matteo RoccaUniversity of InsubriaDepartment of [email protected], [email protected]

MS21

On the Notion of Approximate Strict Solution inSet-valued Optimization via the Set Solution Cri-terion

This talk is concerned with set-valued optimization prob-lems. A new concept of approximate strict solution basedon coradiant sets and the set optimality criterion is intro-duced. Then, the behavior of these approximate solutionswhen the error tends to zero is studied. Finally, some exis-tence results are obtained through scalarization processes.

Cesar GutierrezDepartamento de Matematica AplicadaUniversidad de [email protected]

Bienvenido JimenezUniversidad Nacional de Educacion a [email protected]

Vicente NovoUniversidad Nacional de Educacion a [email protected]

Lionel ThibaultD’epartement des Sciences Math

OP11 Abstracts 117

’ematiquesUniversit’e de Montpellier [email protected]

MS21

Bishop-Phelps Cones

For Bishop-Phelps (BP) cones various properties are pre-sented in normed spaces. Representations of the interiorand the interior of the dual cone of a BP cone are given.A characterization of the reflexivity of a Banach space isformulated using these cones. For an arbitrary cone witha closed bounded base it is shown how an equivalent normcan be constructed so that this cone is representable as aBP cone.

Johannes JahnDepartment of MathematicsUniversity of [email protected]

Truong Xuan Duc HaInstitute of Mathematics of [email protected]

MS21

Conic Regularization for Some Optimization Prob-lems

In recent years new optimality conditions, by means of mul-tiplier rules, were obtained for abstract optimization prob-lems in function spaces where the associated ordering coneof has a nonempty interior. However, it turns out that themultipliers for these problems belong to non-regular spacesof measures. One of the essential requirement of these stud-ies is the validity of a Slater’s type constraint qualification.It is known that Slater’s type constraint qualification isa stringent condition and it does not hold for many im-portant cases of interest. In this talk, we will discuss anew conical regularization technique that gives optimalityconditions without requiring any Slater’s type constraintqualification. The Henig dilating cones is the basic tech-nical tool for this study. Finite element discretization ofthe dilating cone will be discussed and numerical exampleswill be presented.

Akhtar A. KhanRochester Institute of [email protected]

Miguel SamaUniversidad Nacional de Educacion a [email protected]

MS22

Optimal Control of the Cahn-Hilliard VariationalInequality

An optimal control problem governed by Allen-Cahn vari-ational inequality is studied. These problems are phasefield versions of optimal control problems for interfaces andfree boundaries. First order optimality conditions are de-rived by using a penalization/relaxation technique. Wealso use ideas of Hintermuller/Kopacka concerning station-arity concepts for MPECs in function spaces.

Hassan Farshbaf-Shaker

Department of MathematicsUniversity of [email protected]

MS22

Optimal Shape Design Subject to Variational In-equalities

The shape of the free boundary arising from the solutionof a variational inequality is controlled by the shape of thedomain where the variational inequality is defined. Shapeand topological sensitivity analysis is performed for theobstacle problem and for a regularized version of its primal-dual formulation. The shape derivative for the regularizedproblem is defined and converges to the solution of a linearproblem. These results are applied to the electrochemicalmachining problem.

Antoine LaurainKarl-Franzens University of Graz, [email protected]

MS22

A Parabolic MPEC Approach to the Calibration ofAmerican Options Pricing

An inverse problem in the pricing of American options isconsidered. The problem is formulated as an MPEC prob-lem in function space. First-order optimality conditionsof C-stationarity-type are derived. The discrete optimalitysystem is solved numerically by using an active-set-Newtonsolver with feasibility restoration.

Hicham TberDepartment of MathematicsSchool of Science and Technology [email protected]


MS22

Optimal Control of Mixed Variational Inequalities

In this talk some theoretical and numerical aspects on theoptimal control of variational inequalities of the secondkind will be presented. A special kind of regularizing func-tions with an active-inactive set structure will be intro-duced and its importance for the obtention of sharp neces-sary conditions will be highlighted. In addition, the designof second order numerical methods, both globally and lo-cally convergent, for the solution of the control problemswill be discussed.

Juan Carlos de los ReyesEscuela Politecnica Nacional QuitoQuito, [email protected]

MS23

Approximating Convex Hulls of Planar Quartics

Planar quartics are among the simplest examples of al-gebraic sets for which computing the convex hull is non-trivial, and for which applying sums of squares tech-niques and other criteria for semidefinite programming-representability is reasonable. However, even in this simple

118 OP11 Abstracts

case, the behavior of these methods is not entirely under-stood. In this talk we will use these objects as an illus-tration of the techniques, giving a brief survey of what isknown and showing, for this particular case, a nice geomet-ric characterization of the first sums of squares relaxations.

Joao GouveiaUniversity of [email protected]

MS23

A New Look at Nonnegativity and Polynomial Op-timization

We provide a new characterization of nonnegativity of acontinuous function f on a closed and non necessarily com-pact set K of Rn. When f is a polynomial this characteri-zation specializes and provides a hierarchy of nested outerapproximations (Ck) of the convex cone C(K; d) of polyno-mials of degree at most d, nonnegative on K. Each convexcone Ck is a spectrahedron in the coefficients of f with nolifting. In addition, for a fixed known f , checking mem-bership in Ck reduces to solving a generalized eigenvalueproblem for which specialized softwares are available.

Jean B. LasserreLAAS CNRS and Institute of [email protected]

MS23

The Central Path in Linear Programming

The central curve of a linear program consists of the centralpaths for optimizing over any region in the arrangement ofconstraint hyperplanes. We determine the degree, genusand defining ideal of this curve, thereby answering a 1989question of Bayer and Lagarias. Refining work of Dedieu,Malajovich and Shub, we bound the total curvature of cen-tral paths, and we construct instances with many inflectionpoints. Joint work with Jesus DeLoera and Cynthia Vin-zant.

Bernd SturmfelsUniversity of California , [email protected]

MS23

Convergence Theory of Successive Convex Re-laxation Methods for Optimization over Semi-Algebraic Sets

I will discuss various techniques (new and old) used in con-vergence proofs for successive convex relaxation methodsapplied to optimization problems expressed as maximiza-tion of a linear function over a finite set of polynomial in-equality constraints. I will focus on convergence rates andspecially structured nonconvex optimization problems.

Levent TuncelUniversity of WaterlooDept. of Combinatorics and [email protected]

MS24

Piecewise Quadratic Approximations in Convex

Numerical Optimization

We present a proximal bundle method for convex nondif-ferentiable minimization where the model is a piecewisequadratic convex approximation of the objective function.Unlike standard bundle approaches, the model only needsto support the objective function from below at a prop-erly chosen subset of points, as opposed to everywhere.We provide the convergence analysis for the algorithm,with a general form of master problem which combinesfeatures of trust-region stabilization and proximal stabi-lization, taking care of all the important practical aspectssuch as proper handling of the proximity parameter andof the bundle of information. Numerical results are alsoreported.

Annabella AstorinoIstituto di Calcolo e Reti ad Alte Prestazioni - [email protected]

Antonio FrangioniDipartimento di InformaticaUniversity of [email protected]

Manlio GaudiosoDipartimento di Elettronica Informatica e SistemisticaUniversita della Calabria, [email protected]

Enrico GorgoneDipartimento di Elettronica Informatica e SistemisticaUniversita della [email protected]

MS24

New Discrete Gradient Limited Memory BundleMethod for Derivative Free Nonsmooth Optimiza-tion

A new derivative free method is developed for solvingunconstrained nonsmooth optimization problems. Themethod is based on the discrete gradient method byBagirov et.al. and the limited memory bundle method bythe author. The new method uses a bundle of discrete gra-dients to approximate the subdifferential of a nonsmoothfunction. The size of the bundle is kept low by the proce-dure similar to the limited memory bundle method. More-over, the limited memory approach is used to limit theneeded number of operations and the storage space. Thecomparison to some existing methods is given.

Napsu KarmitsaDepartment of MathematicsUniversity of [email protected]

Adil BagirovCIAO, School of ITMS,The University of [email protected]

MS24

Science Fiction in Nonsmooth Optimization

In the 1970’s Lemarechal found that a quasi-Newtonmethod for smooth optimization performed well on somenonsmooth test functions. This was confirmed by Lewisand Overton in 2008. In the 1980’s Lemarechal said that

OP11 Abstracts 119

“Superlinear convergence in nonsmooth optimization is sci-ence fiction”. We discuss the current state of affairs forrapid convergence, based on the U-Hessian of Lemarechal,Oustry and Sagastizabal, and give a BFGS VU -algorithmthat appears to show the achievement of science fiction.

Robert MifflinWashington State [email protected]

Claudia SagastizabalCEPEL (Electric Energy Research Center)[email protected]

MS24

The Proximal Chebychev Center Cutting Plane Al-gorithm for Convex Additive Functions

The recent algorithm based on Chebychev centers proposedrecently [Math. Prog., 119, pp. 239-271, 2009] for con-vex nonsmooth optimization, is extended to the case ofadditive functions. We highlight aspects where this ex-tension differs from the aggregate case. We consider twodifferent nonlinear multicommodity flows applications intelecommunications to assess the method. The numericalexperiments also include some comparison with a proximalbundle algorithm.

Adam OuorouFrance Telecom R&D-Orange [email protected]

MS25

Separation and Relaxation for Completely PositiveMatrices

The cone C of completely positive (CP) matrices is im-portant for globally solving many NP-hard quadratic pro-grams. We construct a conceptual separation algorithm forC based on optimizing over smaller CP matrices, which inparticular yields a concrete separation algorithm for 5 × 5CP matrices. The separation algorithm also motivates anew class of tractable relaxations for C, each of which im-proves a standard polyhedral-semidefinite relaxation. Therelaxation technique can further be applied recursively toobtain a new hierarchy of relaxations, and for constant re-cursive depth, the hierarchy is tractable.

Samuel BurerUniversity of IowaDept of Management [email protected]

Hongbo DongDepartment of MathematicsUniversity of [email protected]

MS25

Symmetric Tensor Approximation Hierarchies forthe Completely Positive Cone

In this work we construct two tensor-structured approxi-mation hierarchies for the completely positive cone. Weshow they correspond to dual cones of two known approxi-mation hierarchies for the copositive cone, one being poly-hedral and the other being semidefinite. As an application,

we construct primal optimal solutions with tensor liftingsof a class of linear programming bounds for the stabilitynumber of a graph.

Hongbo DongDepartment of MathematicsUniversity of [email protected]

MS25

Projections onto the Copositive Cone, and Appli-cations

In this talk we present an algorithm for the projection of amatrix A onto the copositive cone C. By projecting A ontoa sequence of polyhedral inner and outer approximationsof C, we can approximate the projection of A onto C witharbitrary precision. Furthermore we consider projectionsonto the completely positive cone, which is the dual coneof C, and we discuss two applications.

Julia SponselUniversity of [email protected]

Mirjam DuerTU [email protected]

MS25

Computational Experience with Polyhedral Ap-proximations of Copositive Programs

Relying on the previous results in the literature, the authorrecently proposed hierarchies of inner and outer polyhedralapproximations of the copositive cone. Using these approx-imations, two sequences of increasingly sharper lower andupper bounds can be computed for the optimal value ofa copositive program. Under mild assumptions, both se-quences converge to the optimal value in the limit. Wepresent computational results in an attempt to shed lighton the performance of these approximations in practice.

E. Alper YildirimKoc [email protected]

MS26

New Inequalities for Piecewise Linear Optimizationand Mixed-integer Nonlinear Programming

We give new valid inequalities for the piecewise linear op-timization (PLO) knapsack polytope. Then, we presentthe results of our extensive computational study on theiruse on branch-and-cut to solve PLO, as well as nonconvexnonliear and mixed-integer nonlinear programming

Ismael De Farias, Rajat Gupta, Ernee KozyreffTexas [email protected], [email protected],[email protected]

Ming [email protected]

120 OP11 Abstracts

MS26

Strong Polyhedral Relaxations for Multilinear Pro-grams

We study methods for obtaining polyhedral relaxations ofproblems containing multiple multilinear terms. The goalis to obtain a formulation that is more compact than theconvex hull formulation, but yields tighter relaxations thanthe term-by-term or McCormick relaxation. We presentpromising computational results for an approach based ongrouping the variables into subsets that cover all multilin-ear terms in the problem.

James LuedtkeUniversity of Wisconsin-MadisonDepartment of Industrial and Systems [email protected]


Mahdi NamazifarUniversity of [email protected]

MS26

On the Chvatal-Gomory Closure of a CompactConvex Set

In this talk, we show that the Chvatal-Gomory closureof any compact convex set is a rational polytope. Thisresolves an open question of Schrijver 1980 for irrationalpolytopes, and generalizes the same result for the case ofrational polytopes (Schrijver 1980), rational ellipsoids (Deyand Vielma 2010) and strictly convex bodies (Dadush, Deyand Vielma 2010).

Juan Pablo VielmaUniversity of [email protected]

Daniel Dadush, Santanu S. DeyGeorgia Institute of [email protected], [email protected]

MS27

Towards Optimal Newton-Type Algorithms forNonconvex Smooth Optimization

We consider a general class of second-order methods forunconstrained minimization that includes Newton’s, inex-act linesearch, cubic regularization and some trust-regionvariants. For each algorithm in this class, we exhibit anexample of a bounded-below objective with Lipschitz con-tinuous gradient and Hessian such that the method takesat least O(ε−�/∈) function-evaluations to drive the gradi-ent below ε. Thus cubic regularization has (order) optimalworst-case complexity amongst the methods in this class.

Coralia CartisUniversity of EdinburghSchool of [email protected]

Nick GouldNumerical Analysis Group

Rutherford Appleton [email protected]

Philippe L. TointThe University of NamurDepartment of [email protected]

MS27

On Sequential Optimality Conditions for Con-strained Optimization

This talk is based in joint papers with R. Andreani, G.Haeser and B. F. Svaiter. We are concerned with first-order necessary conditions for smooth constrained opti-mization. A feasible point satisfies a sequential conditionif there exists a sequence that converges to it and fulfillssome computable property. These conditions are useful toanalyze algorithms and to provide stopping criteria. Usu-ally, sequential conditions exhibit an Approximate-KKTform and are satisfied by local minimizers independentlyof constraint qualifications.

Jose Mario [email protected]

MS27

Cubic Regularization Algorithm and ComplexityIssues for Nonconvex Optimization

We consider regularization methods for the nonconvex un-constrained and convexely constrained optimization prob-lems. We review known convergence results their remark-able complexity properties, that is the number of functionevaluations that are needed for the algorithm to producean epsilon-critical point. We also discuss the complexity ofthe steepest-descent and Newton’s methods in the uncon-strained case and report surprising conclusions regardingtheir relative complexity. We also indicate why the cubicrelaxation method (ARC) is remarkable and how resultsobtained for this method may be extended to first-orderand DFO algorithms.


Coralia CartisUniversity of EdinburghSchool of [email protected]

Nick GouldNumerical Analysis GroupRutherford Appleton [email protected]

MS27

Back to the Future: Revisiting the Central Path

Since the mid-1980s—the beginning of modern interior-point methods—the central path has played a major con-ceptual and computational role in nonlinear optimization.But the same objects (curves of local minimizers of penaltyand barrier functions) were studied during the 1960s and1970s under different names. Reverting temporarily to the

OP11 Abstracts 121

earlier interpretations, this talk will examine interestingand useful properties of the central path that have tendedto be overlooked in recent years, including the implicationsof a non-tangential approach to the solution and implicitidentification of the active set.

Margaret H. WrightNew York UniversityCourant Institute of Mathematical [email protected]

MS28

Control of Glucose Balance in ICU Patients

Consistent tight blood sugar control in critically ill patientshas proven elusive. Properly accounting for the satura-tion of insulin action and reducing the need for frequentmeasurements are important aspects in intensive insulintherapy. In this talk we present the composite metabolicmodel Glucosafe by Pielmeier et al. (Computer Methodsand Programs in Biomedicine, 97:211-222, 2010) that inte-grates models and parameters from normal physiology andaccounts for the reduced rate of glucose gut absorption andsaturation of insulin action in patients with reduced insulinsensitivity. It is a system of non-linear ordinary differen-tial equations with randomly perturbed parameters whoseoptimal control is of main focus.

Nicole MarheinekeFAU [email protected]

Thomas CibisTU Kaiserslautern / Fraunhofer [email protected]

Ulrike PielmeierAalborg [email protected]

MS28

Model Reduction, Simulation and Optimization ofa Load Change for a Molten Carbonate Fuel Cell

The ability of fast and save load changes is very importantfor stationary power plants powered by molten carbonatefuel cells. A hierachy of realistic and validated models ex-ist. They consist of upto 28 PDEs of parabolic and hyper-bolic type, some equations are degenerated. Part of theboundary conditions are given by a DAE. Numerical sim-ulation and optimization results are presented. We com-pare especially some recently via model reduction devel-oped model variants with existing models.

Armin RundUniversity of Bayreuth,Department of [email protected]

Kurt ChudejUniversity of Bayreuth, Lehrstuhl f. [email protected]

Johanna KerlerUniversity of [email protected]

MS28

The Use of a Generalized Fisher Equation andGlobal Optimization in Chemical Kinetics

A generalized Fisher equation (GFE) relates the timederivative of the average of the intrinsic rate of growthto its variance. The GFE is an exact mathematical resultthat has been widely used in population dynamics and ge-netics, where it originated. Here we demonstrate that theGFE can also be useful in other fields, specifically in chem-istry, with models of chemical reaction systems for whichthe mechanisms and rate coefficients correspond reason-ably well to experiments. The discrepancy of experimentaldata with the GFE can be used as an optimization crite-rion for the determination of rate coefficients in a givenreaction mechanism. We illustrate this approach with twoexamples, the chloriteiodide and the Oregonator systems.

John RossStanford UniversityPalo Alto, [email protected]

Alejandro F. Villaverde, Julio R. BangaIIM-CSICVigo, [email protected], [email protected]

Federico Moran, Sara VazquezUniversidad Complutense de MadridMadrid, [email protected], [email protected]

MS29

Direct MultiSearch: A New DFO Approach forMultiple Objective Functions

DMS is a novel derivative-free algorithm for multiobjectiveoptimization, which does not aggregate any of the objec-tive functions. Inspired by the search/poll paradigm ofdirect-search, DMS uses the concept of Pareto dominanceto maintain a list of nondominated points, from which thenew poll centers are chosen. The aim is to generate asmany Pareto points as possible from the polling procedureitself, while keeping the whole framework general to ac-commodate other disseminating strategies.

A. L. CustodioNew University of LisbonDepartment of [email protected]

J. F. A. MadeiraTechnical University of [email protected]

A. I. F. VazUniversity of [email protected]

L. N. VicenteUniversity of [email protected]

MS29

A Principled Stochastic Viewpoint on Derivative-

122 OP11 Abstracts

Free Optimization

We consider numerical black-box optimization with littleassumptions on the underlying objective function. Fur-ther, we consider sampling from a distribution to obtainnew candidate solutions. Under mild assumptions, solv-ing the original unknown optimization problem coincideswith optimizing a parametrized family of distributions ofour choice. Following seminal works of Wierstra and Glas-machers, we can now derive a gradient descend on thedistribution manifold in a derivative-free problem context.For multivariate normal distributions this leads to a sim-plified instantiation of CMA-ES.

Nikolaus HansenINRIA-Saclay, Universite Paris-Sud, [email protected]

MS29

Derivative-Free methods for Mixed-Integer Opti-mization Problems

We consider the problem of minimizing a continuously dif-ferentiable function of several variables where some of thevariables are restricted to take integer values. We assumethat the first order derivatives of the objective functioncan be neither calculated nor approximated explicitly. Wepropose an algorithm convergent to points satisfying suit-able stationarity conditions. Integer variables are tackledby a local search-type approach. Numerical results on adifficult real application are presented and sustain the pro-posed method.

Stefano LucidiUniversity of [email protected]

Giampaolo LiuzziCNR - [email protected]

Francesco RinaldiUniversity of [email protected]

MS29

Optimization With Some Derivatives

What is the value of knowing some partial derivatives insimulation-based optimization? We attempt an answerthrough our experience extracting additional structure onproblems consisting of both blackbox and algebraic com-ponents. These problems include knowing derivatives: ofsome residuals in nonlinear least squares problems, of somenonlinear constraints, and with respect to a subset of thevariables. In each case we use quadratic surrogates tomodel both the blackbox and algebraic components.

Stefan WildArgonne National [email protected]

Jorge J. MoreArgonne National LaboratoryDiv of Math & Computer [email protected]

MS30

Randomized Dimensionality Reduction for Full-waveform Inversion

One of the major problems with full-waveform inversionis the requirement of solving large systems of discretizedPDE’s for each source (right-hand side). For 3-D prob-lems, this requirement is computationally prohibitive. Toaddress this fundamental issue, we propose a random-ized dimensionality-reduction strategy motivated by recentdevelopments in stochastic optimization and compressivesensing. In this formulation, conventional Gauss-Newtoniterations are replaced by dimensionality-reduced sparse re-covery problems with randomized source encodings.

Felix J. HerrmannSeismic Laboratory for Imaging and ModelingThe University of British [email protected]

Tristan van Leeuwen, Aleksandr Aravkin, Xiang Lithe University of British [email protected], [email protected],[email protected]

MS30

Stochastic Optimization Framework for Design ofProper Orthogonal Decomposition Bases

Numerical solution of large-scale Partial Differential Equa-tions (PDEs) is challenging from various aspects. TheProper Orthogonal Decomposition (POD) method hasbeen commonly employed for projection of the solutioninto a lower dimensional subspace. Despite the popular-ity of the approach, its utility was hitherto limited due tothe specificity of the POD basis to the model parametersand the corresponding right-hand-side it has been obtainedfrom. In this study we propose a framework for the designof POD bases. The design problem is formulated as a non-linear optimization problem with PDEs and reduced orderPDE constraints. In order to account for model space vari-ability with respect to the model and the right-hand-side,we resort to a Stochastic Sampling Average (SSA) formu-lation. Since the design process can be computationallyintensive, we accelerate the procedure by the incorpora-tion of stochastic trace estimators. Numerical studies, ad-dressing the solution of large-scale problems, indicate thesuperiority of the designed bases upon their conventionalcounterparts.

Lior HoreshBusiness Analytics and Mathematical SciencesIBM TJ Watson Research [email protected]


Marta D’EliaMathCS, Emory [email protected]

MS30

Integration of Data Reduction Techniques and Op-timization Algorithms

We present a comparison of optimization algorithms that

OP11 Abstracts 123

enable the use of (nonlinear) data reduction techniquesin parameter estimation for partial differential equations.The comparison includes both full-space and reduced-spaceformulations and algorithms based on these approaches. Inorder to evaluate their performance, we provide a series ofnumerical experiments related to a data reduction tech-nique based on compressed sensing.

Denis Ridzal, Joseph YoungSandia National [email protected], [email protected]

MS30

Compressed Sensing in a Finite Product of HilbertSpaces

We present an extension of the theory of compressed sens-ing to finite products of Hilbert spaces. This enables theuse of compressed sensing in domains such as Sobolovspaces which are the natural setting for partial differen-tial equations (PDEs). Using this extension, we reducethe cost of solving systems of PDEs where each equationuses identical differential operators. Our result allows areduction in the computational cost of an important classof parameter estimation problems.

Joseph Young, Denis RidzalSandia National [email protected], [email protected]

MS31

Optimization over a Pareto Set in Multi-ObjectiveControl Problems

My talk deals with the problem of optimizing a nonsmoothreal valued function over the efficient (Pareto) control pro-cesses set associated to a multi-objective control problem(grand coalition of a multi-player cooperative differentialgame). This problem may be considered as an attempt tohelp a decision maker in his choice of an efficient controlprocess, because the efficient set is often very large (infi-nite) and not explicitly described.

Henri BonnelERIM, University of New [email protected]

MS31

Optimality Conditions for Vector OptimizationProblems with Variable Ordering Structures

Motivated by some recent applications e.g. in medical im-age registration we discuss vector optimization problemswith a variable ordering structure. This structure is as-sumed to be given by a cone-valued map which associatesto each element of the space a cone of preferred or domi-nated directions. For the case when the values of the cone-valued map are Bishop-Phelps cones we obtain for the firsttime scalarizations and based on that Fermat and Lagrangemultiplier rule.

Gabriele EichfelderDepartment of MathematicsUniversity of [email protected]

Truong Xuan Duc HaInstitute of Mathematics of [email protected]

MS31

Geometric Duality for Convex Vector OptimizationProblems

Recently, a geometric duality theory for linear vector op-timization problems was developed. That theory providesan inclusion-reversing one-to-one correspondence between’optimal’ faces of the image sets of the primal and the dualproblem. We will extend this theory to the more generalcase of convex vector optimization problems.

Frank HeydeInstitute of MathematicsUniversity of [email protected]

MS31

Algorithms for Linear Vector Optimization Prob-lems

In 1998, Benson proposed a very efficient method to solvelinear vector optimization problems, called outer approx-imation method. The idea is to construct the minimalpoints in the outcome space. Geometric duality for mul-tiobjective linear programming can be used to derive adual variant of Benson’s outer approximation algorithm.Moreover, this duality theory can be used to obtain innerapproximations. We propose an extension of Benson’s al-gorithm as well as its dual variant which applies also toproblems with an unbounded feasible set. This means thatarbitrary linear vector optimization problems with the or-dinary ordering cone and having at least one minimal ver-tex can be solved.

Andreas LoehneInstitute of MathematicsUniversity of [email protected]

MS32

On Hilbert’s Theorem about Nonnegative Polyno-mials in Two Variables

In 1893 Hilbert showed that for every nonnegative bivari-ate polynomial p of degree 2d there exists a nonnegativebivariate polynomial q of degree 2d − 4 such that pq is asum of squares. Hilbert’s proof is not well understood, andthere are no modern expositions of it. As a consequence,the result itself is largely forgotten. I will explain a newproof of this result.

Greg BlekhermanUniversity of California, San [email protected]

MS32

Moment Matrices and the Tensor DecompositionProblem

In this talk, we will describe some connections between ten-sor decomposition, algebraic duality and moment matrices.We will show how exploiting the structure of these matri-ces can help solving the decomposition problem for generalor symmetric tensors. This approach will be illustrated bysome applications in geometric modelling.

Bernard MourrainINRIA Sophia [email protected]

124 OP11 Abstracts

MS32

Inverse Moment Problem for n-dimensional Poly-topes

The inverse moment problem asks to find the measure given(some of) its moments. It is well-studied in the case ofthe measures supported on a plane polygon, and can besolved exactly for convex polygons. In bigger dimensions,however, it was not known how to solve it exactly even inthe case of uniform measures supported on simple convexpolytopes, and all the known approximate methods reliedon slicing the unknown body into a large number of 2-dimensional cylinders. We present a novel approach thatproduces exact answers, as well as is it capable of approxi-mate solving. Along the way we show that O(N) moments,for N being the number of vertices of the convex polytope,suffice to reconstruct it. Joint work with N. Gravin, J.Lasserre, and S. Robins

Dmitrii PasechnikNanyang Technological [email protected]

MS32

Using Sums of Squares and Semidefinite Program-ming to Approximate Amoebas

Amoebas are the logarithmic images of algebraic vari-eties. We present new techniques for tackling computa-tional problems on amoebas (such as the membership prob-lem) based on sums of sums of squares techniques andsemidefinite programming. Our method yields polynomialidentities as certificates of non-containedness of a point inan amoeba. As main theoretical result, we establish somedegree bounds on the polynomial certificates. Moreover,we provide some actual computations of amoebas based onthe sums of squares approach. (Joint work with Timo deWolff.)

Thorsten TheobaldJ.W. Goethe-UniversitatFrankfurt am Main, [email protected]

MS33

Immunizing Conic Quadratic Optimization Prob-lems Against Implemention Errors

We show that the robust counterpart of a convex quadraticconstraint with ellipsoidal implementation error is equiva-lent to a system of conic quadratic constraints. To provethis result we first derive a sharper result for the S-lemmain case the two matrices involved are simultaneously di-agonizable. This extension of the S-lemma may also beuseful for other purposes. We also extend the results tothe case of conic quadratic constraints with implementa-tion error. Several applications are discussed, e.g., designcentering, robust linear programming with both parameteruncertainty and implementation error, and quadratic deci-sion rules for the adjustable robust optimization problem.

Dick Den HertogTilburg UniversityFaculty of Economics and Business [email protected]

Aharon Ben-TalTechnion - Israel Institue of Technology

[email protected]

MS33

Robust Optimization Made Easy with ROME

We introduce ROME, a MATLAB-based algebraic mod-eling toolbox for modeling a class of robust optimizationproblems. ROME serves as an intermediate layer betweenthe modeler and optimization solver engines, allowing mod-elers to express robust optimization problems in a math-ematically meaningful way. Using modeling examples, wediscuss how ROME can be used to model and analyze ro-bust optimization problems. ROME is freely distributedfor academic use from www.robustopt.com.

Joel GohStanford [email protected]


MS33

Robust Optimization of Nonlinear Constrained Dy-namic Systems

We present a technique to solve robust optimal controlproblems for nonlinear dynamic systems in a conservativeapproximation. Here, the nonlinear dynamic system is af-fected by an uncertainty whose L-infinity norm is knownto be bounded. In a second part of the talk, we addressthe discretized problem, a min-max nonlinear program, bya novel variant of SQP type methods, sequential bi-levelquadratic programming. Both techniques are illustratedby applying them to numerical examples.

Boris HouskaKU [email protected]


MS33

Distributionally Robust Joint Chance Constraintswith Second-Order Moment Information

We develop tractable SDP-based approximations for dis-tributionally robust chance constraints, assuming that onlythe first- and second-order moments and the support of theuncertain parameters are given. We prove that robust in-dividual chance constraints are equivalent to Worst-CaseConditional Value-at-Risk constraints. We also developa conservative approximation for joint chance constraints,whose tightness depends on a set of scaling parameters.We show that this approximation becomes exact when thescaling parameters are chosen optimally.

Steve Zymler, Daniel Kuhn, Berc RustemImperial College [email protected], [email protected],[email protected]

OP11 Abstracts 125

MS34

Building a Completely Positive Factorization

Using a bordering approach, and building upon an alreadyknown factorization of a principal block, we establish suffi-cient conditions under which we can extend this factoriza-tion to the full matrix. Simulations show that the approachis promising also in higher dimensions, provided there is nogap in the cp-rank. Also, a construction of instances withguaranteed high cp-rank is presented.


MS34

Checking if a Sparse Matrix is Completely Positive

The completely positive cone is useful in optimization as itcan be used to create convex formulations of NP-completeproblems. In this talk we discuss the problem of checkingif a sparse matrix is completely positive and finding its cp-rank when it is. We present a linear time algorithm forpreprocessing a matrix to reduce the problem. For spe-cial types of matrices, for example acyclic matrices, thisalgorithm in fact solves the problem.

Peter DickinsonUniversity of [email protected]

MS34

A Copositive Approach for Perfect Graphs

If equality between the chromatic number and the clicknumber of a graph holds, and if the same is true for anyof its induced subgraphs, the graph is called perfect. Re-cently, in their celebrated paper ”The strong perfect graphtheorem”, Chudnovsky, Robertson, Seymour and Thomasproved that a graph is perfect if and only if it does not con-tain an odd hole or odd antihole (with at least 5 nodes) asan induced subgraph. Shortly after, Chudnovsky, Corne-jouls, Liu, Seymour and Vuskovic proved that recognitionof perfect graphs can also be done in polynomial time.If a graph is perfect, its chromatic number can be deter-mined by a polynomial time algorithm. It was proven byGrtschel, Lovsz and Schrijver in late 80’s, and their algo-rithm is based on semidefinite programming. Nevertheless,one of the most intriguing open questions related to perfectgraphs is the design of pure combinatorial polynomial timealgorithm for determining their chromatic numbers. Wepresent some copositive formulations for the clique num-ber and the chromatic number of a graph, and study theirconnections for the class of perfect graphs. We show howsuch an approach can link the result of Grtschel, Lovsz andSchrijver with pure combinatorial approaches. Still, one ofthe most intriguing questions of combinatorial optimiza-tion is the existence of pure combinatorial algorithm. Wewill revisit some known mathematical programming formu-lations for the stable set number

Nebojsa GvozdenovicUniversity of Novi [email protected]

MS34

On the Set-Semidefinite Representation of Noncon-

vex Quadratic Programs with Cone Constraints

We present a generalization of the well-known result statingthat any non-convex quadratic problem over the nonneg-ative orthant with some additional linear and binary con-straints can be rewritten as linear problem over the cone ofcompletely positive matrices. The generalization is done byreplacing the nonnegative orthant with an arbitrary closedconvex cone. This set-semidefinite representation resultimplies new semidefinite lower bounds for quadratic prob-lems over several Bishop-Phelps cones, presented in thetalk

Janez PovhFaculty of Information Studies in Novo [email protected]

Gabriele EichfelderDepartment of MathematicsUniversity of [email protected]

MS35

Robust Independence Systems

This talk discusses the robustness for independence sys-tems, which is a natural generalization of the greedy prop-erty of matroids. An independent set X is called α-robustif for any k, it includes an α-approximation of the maxi-mum k-independent set (i.e., an independent set with sizeat most k). We show every independence system F has a

1/√

μ(F)-robust independent set, where μ(F) denotes theexchangeability of F . Our result provides better boundsfor various independence systems.

Naonori Kakimura, Kazuhisa MakinoUniversity of [email protected],[email protected]

MS35

A Primal-Dual Algorithm for Lattice Polyhedra

Hoffman and Schwartz developed 1978 the Lattice Poly-hedron model and proved that it is totally dual inte-gral (TDI), and so has integral optimal solutions. Themodel generalizes many important combinatorial optimiza-tion problems, but has lacked a combinatorial algorithm.We developed the first combinatorial algorithm for thisproblem, based on the Primal-Dual Algorithm framework.The heart of our algorithm is an efficient routine that usesan oracle to solve a restricted abstract cut packing/shortestpath subproblem. This plus a standard scaling techniqueyields a polynomial combinatorial algorithm. The talk willcover an introduction to the Lattice Polyhedron model, aswell as a description of this primal-dual algorithm.

Britta PeisT. U. [email protected]

S. Thomas McCormickSauder School of Business, Vancouver, [email protected]

MS35

Principal Partition and the Matroid Secretary

126 OP11 Abstracts

Problem

The goal in the Random Assignment Model of Matroid Sec-retary Problem is to select a maximum weight independentset of elements that arrive online in a random order. Theweights are chosen by an adversary but are assigned ran-domly to the elements from the matroid ground set. Byexploiting the principal partition of a matroid and its de-composition into uniformly dense minors we give the firstconstant factor competitive algorithm for this problem.

Jose A. [email protected]

MS35

Generic Rigidity Matroids with Dilworth Trunca-tions

We prove that the linear matroid that defines generic rigid-ity of d-dimensional body-rod-bar frameworks (i.e., struc-tures consisting of disjoint bodies and rods linked by bars)

can be obtained from the union of(

d+12

)graphic matroids

by applying variants of the Dilworth truncation nr times,where nr denotes the number of rods. This leads to analternative proof of Tay’s combinatorial characterizationsof generic rigidity of rod-bar frameworks and that of iden-tified body-hinge frameworks.

Shin-ichi TanigawaKyoto [email protected]

MS36

An Outer-Inner Approximation for SeparableMINLP

We study Mixed Integer Nonlinear programs, where allnonlinear functions are convex and separable. One of themost efficient approaches to solve Mixed Integer Nonlin-ear programs is Outer Approximation. We show that evenwhen all nonlinear function are separable Outer Approxi-mation based algorithms can require the generation of anexponential number of iterations to converge. We propose acure that exploits the separability of the functions. We alsocombine the modified outer approximation with an innerapproximation scheme in order to obtain good feasible so-lution. We test the practical effectiveness of our approachon an application in the telecommunications industry.

Pierre BonamiLaboratoire d’Informatique Fondamentale de [email protected]

Hassan HijaziLIX, Ecole Polytechnique, Palaiseau, [email protected]

Adam OuorouFrance Telecom R&D-Orange [email protected]

MS36

Maximizing Expected Utility in the Presence ofDiscrete Decisions

We consider the problem of maximizing expected logarith-mic utility in conjunction with a linear objective function

over a mixed integer polyhedral set. We solve the resultingproblems using an outer approximation approach, wherewe apply an SQP-based algorithm to solve the nonlinearsubproblems. Computational results for large-scale portfo-lio optimization problems are presented both for the con-tinuous as well as for the mixed integer setting.

Sarah DrewesTechnische Universitat Darmstadt, Department ofMathematicsUniversity of California - [email protected]


MS36

Optimistic MILP Approximations of Non-LinearOptimization Problems

We present a new piecewise-affine approximation of non-linear optimization problems that can be seen as a general-ization of the classical Union Jack triangulation. Roughlyspeaking, it is a generalization because it leaves more de-grees of freedom to define any point as a convex combina-tion of the samples. As an example, for the classical case ofapproximating a function of two variables, a convex com-bination of four points instead of only three is used. Be-cause a plane is defined by only three independent points,the approximation obtained by triangulation is uniquelydetermined, while different approximations are possible inour case. If embedded in a Mixed-Integer Linear Program-ming (MILP) model the choice among those alternatives is(optimistically) guided by the objective function. An ad-vantage of the new approximation within an MILP is thatit requires a significant smaller number of additional binaryvariables and the logarithmic representation of these vari-ables recently proposed by Vielma and Nemhauser can beapplied. We show theoretical and computational evidenceof the quality of the approximation and its impact withinMILP models.

Andrea Lodi, Claudia D’AmbrosioUniversity of [email protected], [email protected]

Silvano MartelloDEIS, University of [email protected]

Riccardo RovattiDEIS and ARCES, University of [email protected]

MS36

Global Optimization of Equilibirum ConstrainedNetworks

Network flows are generally governed by an equilibriumprinciple such as Kirchoffs Laws in electrical networks,Wardrop Principle in transportation networks and Lawsof Static Equilibrium in structural networks. All of aboveproblem classes can be reduced to networks with nonlin-ear resistances. Earlier formulations cast the problem as anon-convex and non-smooth MINLP with no guarantee ofglobal optimality. We present a novel convex MINLP for-mulation and describe an algorithm based on linearizations

OP11 Abstracts 127

for the efficient solution. We also describe a new projectednonlinear cut that can be generalized to the class of Con-vex Disjunctive Programs. Effectiveness of the perspectivecut for this class of problems will also be explored. Re-sults demonstrating the effectiveness of the approach onapplications from literature will be presented.

Arvind RaghunathanUnited Technologies Research [email protected]

MS37

Practical Algorithmic Strategies in Augmented La-grangians

Practical strategies for improving the effectiveness of Aug-mented Lagrangian methods will be discussed in thepresent work. The outer-trust region strategy for deal-ing with the so called greediness phenomenon will be de-scribed. A nonmonotone scheme for increasing the penaltyparameter will also be discussed. Theoretical results willbe presented and numerical evidences of the usefulness ofthe suggested strategies will be analysed.

Ernesto G. BirginDepartment of Computer Science - IMEUniversity of So [email protected]

MS37

Augmented Lagrangian Filter Methods

We introduce a two-phase method for large-scale nonlinearoptimization. In the first phase, projected-gradient itera-tions approximately minimize the augmented Lagrangianto estimate the optimal active set. In the second phase,we solve an equality-constrained QP. An augmented La-grangian filter determines the accuracy of the augmentedLagrangian minimization and promotes global conver-gence. Our algorithm is designed for large-scale optimiza-tion, and we present promising numerical results.


MS37

Local Convergence of Exact and Inexact Aug-mented Lagrangian Methods under the Second-order Sufficiency Condition

We establish local convergence and rate of convergence ofthe classical augmented Lagrangian algorithm (also knownas the method of multipliers) under the sole assumptionthat the dual starting point is close to a multiplier satisfy-ing the second-order sufficient optimality condition. In par-ticular, no constraint qualifications of any kind are needed.Previous literature on the subject required the linear inde-pendence constraint qualification and, in addition, eitherthe strict complementarity assumption or the stronger ver-sion of second-order sufficiency. For sufficiently large valuesof the penalty parameters we prove primal-dual Q-linearconvergence rate, which becomes superlinear if the param-eters are allowed to go to infinity. Both exact and inexactsolutions of subproblems are considered. In the exact case,we further show that the primal convergence rate is of thesame Q-order as the primal-dual rate. Previous assertionsfor the primal sequence all had to do with the the weakerR-rate of convergence (and required the stronger assump-

tions cited above).

Mikhail V. SolodovInst de Math Pura e [email protected]

Damian FernandezFaMAF, Univ. de [email protected]

MS37

Matrix-free Nonlinear Programming for DynamicOptimization

We investigate dynamic optimization problems that appearin nonlinear model predictive control. Such problems canbe represented as parametric variational inequality prob-lems. Aiming for real-time performance in a resource-limited environment, we propose a method that solves in-exactly a quadratic program per step and prove that it sta-bly tracks the optimal manifold. We demonstrate how theapproach can be implemented in an iterative matrix-freeframework by using an augmented Lagrangian approach.

Victor ZavalaArgonne National [email protected]

Mihai AnitescuArgonne National LaboratoryMathematics and Computer Science [email protected]

MS38

Numerical Methods for Model Discrimination inChemistry and Biosciences

If two or more model candidates are proposed to describethe same process and information available does not allowto discriminate between the candidates, new experimentsmust be designed to reject models by lack-of-fit test. Math-ematically this leads to highly structured, complex, mul-tiple experiments, multiple models optimal control prob-lems. Special emphasis is placed on robustification of op-timal designs against uncertainties in model parameters.New numerical methods and applications from chemistryand biosciences will be discussed.

Thorsten Ante, Ekaterina Kostina, Gregor KriwetFachbereich Mathematik und InformatikPhilipps-Universitaet [email protected],[email protected], [email protected]

MS38

Challenges of Parameter Identification for Nonlin-ear Biological and Chemical Systems

Mathematical models ensuring a highly predictive powerare of inestimable value in systems biology. Their applica-tion ranges from investigations of basic processes in livingorganisms up to model based drug design in the field ofpharmacology. For this purpose simulation results have tobe in consistency with the real process, i.e., suitable modelparameters have to be identified minimizing the differencebetween the model outcome and measurement data. Inthis work, graph based methods are used to figure out

128 OP11 Abstracts

if conditions of parameter identifiability are fulfilled. Incombination with network centralities, the structural rep-resentation of the underlying mathematical model providesa first guess of informative output configurations. As atleast the most influential parameters should be identifiableand to reduce the complexity of the parameter identifica-tion process further a parameter ranking is done by Sobol’indices. The calculation of these indices goes along witha highly computational effort, hence monomial cubaturerules are used as an efficient approach of numerical inte-gration. In addition, a joint application of the previouslyintroduced methods enables an online model selection pro-cess, i.e., operation conditions can be derived that makepreviously undistinguishable model candidates distinguish-able. The feature of an online framework is quite attractiveas it avoids the need for additional time consuming exper-iments. All methods are demonstrated for a well knownmotif in signaling pathways, the MAP kinase cascade.

Michael MangoldMax-Planck-Institut fur Dynamik komplexer technischerSystemMagdeburg, [email protected]

Rene SchenkendorfMax-Planck-Institut fuer Dynamik komplexer technischerSysteme, Magdeburg, [email protected]

MS38

Robust Optimal Experimental Design for Modeldiscrimination of Dynamic Biochemical Systems

Finding suitable models of dynamic biochemical systems isan important task in the biosciences. On the one hand acorrect model can explain the underlying mechanisms onthe other hand one can use the model to predict the be-havior of a biological system under various circumstances.We present a computational framework to compute robustoptimal experimental designs for the purpose of model dis-crimination.

Dominik SkandaDepartment of Applied MathematicsUniversity of Freiburg, [email protected]

Dirk LebiedzUniversity of FreiburgCenter for Systems [email protected]

MS39

Preconditioned Conjugate Gradient Method forOptimal Control Problems with Control and StateConstraints

We consider saddle-point problems arising as linearized op-timality conditions in optimal control problems. The effi-cient solution of such systems is a core ingredient in second-order optimization algorithms. In the spirit of Brambleand Pasciak, the preconditioned systems can be turned intosymmetric and positive definite ones with respect to a suit-able scalar product. We focus on the solution of problemswith control and state constraints and provide numericalexamples in 2D and 3D to illustrate the viability of our

approach.

Roland HerzogChemnitz University of [email protected]

Ekkehard W. SachsUniversity of TrierVirginia [email protected]

MS39

All-at-once Solution of Time-dependent PDE-constrained Optimization Problems

Time-dependent partial differential equations (PDEs) playan important role in applied mathematics and many otherareas of science. One-shot methods try to compute the so-lution to these problems in a single iteration that solvesfor all time-steps at the same time. In this talk, we lookat one-shot approaches for the optimal control of time-dependent PDEs and focus on the fast solution of theseproblems. The use of Krylov subspace solvers togetherwith an efficient preconditioner allows for minimal storagerequirements. We solve only approximate time-evolutionsfor both forward and adjoint problem and compute accu-rate solutions of a given control problem only at conver-gence of the overall Krylov subspace iteration. We showthat our approach can give competitive results for a varietyof problem formulations.

Martin StollComputational Methods in Systems and Control TheoryMax Planck Institute for Dynamics of Complex [email protected]

Andrew J. WathenOxford UniversityNumerical Analysis [email protected]

MS39

Preconditioning for An Option Pricing Problem

The pricing of European option using Merton’s model leadsto a partial integro-differential equation (PIDE). The nu-merical solution involves the solution of linear systems withdense coefficient matrices. We use a preconditioned con-jugate gradient method combined with fast Fourier trans-form. The choice of the preconditioners is studied thor-oughly, including estimates for the spectrum and mesh in-dependence of the number of iterates required. The resultsare extended to relevant optimization problem and furtherdiscussed in such a context.

Xuancan YeFB IV - Department of MathematicsUniversity of [email protected]


MS39

Robust Preconditioners for Distributed Optimal

OP11 Abstracts 129

Control of the Stokes Equations

In this talk an optimal control problem for steady stateStokes flow with distributed control is considered. Theoptimal control problem involves a regularization param-eter, say α, in the cost functional. For solving the dis-cretized optimality system, we will present preconditionedKrylov subspace methods whose convergence rate is uni-formly bounded in α.

Walter ZulehnerUniversity of Linz, [email protected]

MS40

Convergence Properties of Evolution Strategies

Evolution strategies (ESs) are stochastic optimization algo-rithms for numerical optimization. In each iteration of anES, internal parameters are updated using the ranking ofcandidate solutions and not their intrinsic objective func-tion value. In this talk, we review linear convergence re-sults for evolution strategies and discuss the consequencesof the rank-based update in terms of lower bounds for con-vergence rates and invariance classes for the set of functionswhere linear convergence holds.

Anne AugerINRIA [email protected]

MS40

Stochastic Second-Order Method for Function-Value Free Numerical Optimization

We review the counterpart of Quasi-Newton methods inevolutionary computation: the covariance matrix adapta-tion evolution strategy, CMA-ES. The CMA-ES adapts asecond-order model of the underlying objective function.On convex-quadratic functions, the resulting covariancematrix resembles the inverse Hessian matrix. Surprisingly,this can be accomplished derivative- and function-valuefree. The CMA-ES reveals the same invariance proper-ties as the Nelder-Mead method, works reliably not only inlow dimension and is surprisingly efficient also on convexand non-convex, highly ill-conditioned problems.

Nikolaus HansenINRIA-Saclay, Universite Paris-Sud, [email protected]

MS40

Theory of Randomized Search Heuristics in Com-binatorial Optimization

We analyze the runtime and approximation quality ofrandomized search heuristics when solving combinatorialoptimization problems. Our studies treat simple local-search algorithms and simulated annealing as well as morecomplex population-based evolutionary algorithms. Thecombinatorial optimization problems discussed include themaximum matching problem, the partition problem andthe minimum spanning tree problem as an example whereSimulated Annealing beats the Metropolis algorithm incombinatorial optimization. Important concepts of theanalyses will be sketched as well.

Carsten WittTechnical University of Denmark

[email protected]

Pietro Simone OlivetoUniversity of [email protected]

MS40

Some Applications of Evolutionary Computation

This talk introduces some applications of evolutionary al-gorithms, including data-driven modelling in astrophysicsand materials engineering, route optimisation for saltingtrucks in winter, multi-objective design of digital filters,software testing resource allocation, redundancy allocationin maximising system reliability, etc. The primary aimof this talk is to illustrate innovative applications of vari-ous randomised search heuristics, rather than trying to becomprehensive.

Xin YaoUniversity of [email protected]

MS42

The Infinite Push: A New Support Vector RankingAlgorithm that Directly Optimizes Accuracy at theAbsolute Top of the List

I will describe a new ranking algorithm called the ‘Infi-nite Push’ that directly optimizes ranking accuracy at theabsolute top of the list. The algorithm is a support vec-tor style algorithm, but due to the different objective, itno longer leads to a quadratic programming problem. In-stead, the dual optimization problem involves l1,∞ con-straints; we solve this using an efficient gradient projectionmethod. Experiments on real-world data sets confirm thealgorithm’s focus on accuracy at the absolute top of thelist.

Shivani AgarwalIndian Institute of [email protected]

MS42

A Graph Theoretical Approach to PreferenceBased Ranking: Survey of Recent Results

I will survey recent results for preference based rankingfrom a graph theoretical perspective, where the problemis known as ”Minimum Feedback Arc-Set”. The followingresults will be highlighted: A simple 3-approximation usingQuickSort, a PTAS by Kenyon and Schudy and a morerecent sub-linear version of the PTAS. Special attentionwill be paid to the important Rank Aggregation case, inwhich the input is a convex combination of permutations.

Nir AilonTechnion Israel Institute of [email protected]

MS42

Bayesian Ranking

I will present several large-scale applications of Bayesianranking algorithms to various domains including (1) gamerranking on Xbox Live (”TrueSkill”), (2) professional chessgamer ranking across their lifetime (”TrueSkill-through-

130 OP11 Abstracts

Time”), (3) research school ranking in the 2008 BritishResearch Assessment Exercise, and (4) ranking of adver-tisements (adPredictor) on Microsoft’s search engine, bing.The key challenge in all these domains is data sparsity perentity - usually there are only O(log(n)) comparisons avail-able for O(n) entities. I will also present an informationtheoretic viewpoint of ranking for evaluating the efficiencyof Bayesian ranking algorithms.

Ralf HerbrichMicrosoft Research [email protected]

MS42

New Models and Methodologies for Group Deci-sion Making, Rank Aggregation, Clustering andData Mining

The aggregate ranking problem is to obtain a ranking thatis fair and representative of the individual decision makers’rankings. We argue here that using cardinal pairwise com-parisons provides several advantages over score-wise or or-dinal models. The aggregate group ranking problem is for-malized as the separation model and separation-deviationmodel and linked to the inverse equal paths problem. Thisnew approach is shown to have advantages over PageRankand the principal eigenvector methods.

Dorit HochbaumIndustrial Engineering and Operations ResearchUniversity of California, [email protected]

MS43

An Efficient Algorithm for Variable Sparsity Ker-nel Learning

We present algorithms and applications for a particularclass of mixed-norm regularization based Multiple KernelLearning (MKL) formulations. The formulations assumethat the given kernels are grouped and employ L1 normregularization for promoting sparsity within each group,and Lp norm for promoting non-sparse combinations acrossgroups. Various sparsity levels in combining the kernels canbe achieved by varying the grouping of kernels—hence wename the formulations as Variable Sparsity Kernel Learn-ing (VSKL) formulations. While previous attempts have anon-convex formulation, here we present a convex formula-tion which admits efficient Mirror-Descent (MD) based al-gorithm, combined with block coordinate descent method.Experimental results show that the VSKL formulations arewell-suited for multi-modal learning tasks like object cate-gorization. Results also show that the MD based algorithmoutperforms state-of-the-art MKL solvers in terms of com-putational efficiency.

Aharon Ben-TalTechnion - Israel Institue of [email protected]

MS43

Robust PCA and Collaborative Filtering: Reject-ing Outliers, Identifying Manipulators

Principal Component Analysis is one of the most widelyused techniques for dimensionality reduction. Neverthe-less, it is plagued by sensitivity to outliers; finding robustanalogs, particularly for high-dimensional data, is criti-

cal. We present an efficient convex optimization-based al-gorithm we call Outlier Pursuit that recovers the exactoptimal low-dimensional subspace, and identifies the cor-rupted points. We extend this to the partially observedsetting, significantly extending matrix completion resultsto the setting of corrupted rows or columns.

Constantine CaramanisThe University of Texas at [email protected]

MS43

Robustness Models in Learning

Robust optimization is a methodology traditionally appliedto handle measurement errors or uncertainty about futuredata in a decision problem. As such, it has a natural placein machine learning applications. In fact, classical learn-ing models such as SVMs or penalized regression can beinterpreted in terms of robustness models. This interpre-tation leads to new insights into important aspects suchas consistency and sparsity of solutions. Building on theseconnections, we show that robust optimization ideas canlead to new, more performant learning models that takeinto account data structure, such as those arising in textclassification, where the data is often boolean or integer-valued. Robustness models can also be used in the contextof a large-scale learning problem with dense data, basedon the idea of thresholding and taking into account theresulting error when solving the learning problem.

Laurent El GhaouiEECS, U.C. [email protected]

MS43

Robust High-Dimensional Principal ComponentAnalysis

We revisit one of the perhaps most widely used statisticaltechniques for dimensionality reduction: Principal Com-ponent Analysis (PCA). In the standard setting, PCA iscomputationally efficient, and statistically consistent, i.e.,as the number of samples goes to infinity, we are guaranteedto recover the optimal low-dimensional subspace. On theother hand, PCA is well-known to be exceptionally brittle– even a single corrupted point can lead to arbitrarily badPCA output. We consider PCA in the high-dimensionalregime, where a constant fraction of the observations inthe data set are arbitrarily corrupted. We show that stan-dard techniques fail in this setting, and discuss some of theunique challenges (and also opportunities) that the high-dimensional regime poses. For example, one of the (many)confounding features of the high-dimensional regime, isthat the noise magnitude dwarfs the signal magnitude, i.e.,SNR goes to zero. While in the classical regime, dimen-sionality recovery would fail under these conditions, sharpconcentration-of-measure phenomena in high dimensionsprovide a way forward. Then, for the main part of the talk,we propose a High-dimensional Robust Principal Compo-nent Analysis (HR-PCA) algorithm that is computation-ally tractable, robust to contaminated points, and easilykernelizable. The resulting subspace has a bounded devia-tion from the desired one, for up to 50% corrupted points.No algorithm can possibly do better than that, and thereis currently no known polynomial-time algorithm that canhandle anything above 0%. Finally, unlike ordinary PCAalgorithms, HR-PCA has perfect recovery in the limiting

OP11 Abstracts 131

case where the proportion of corrupted points goes to zero.

Shie MannorElectrical [email protected]

MS44

Copositivity and Constrained Fractional QuadraticProblems

Completely Positive (CpPP) and Copositive Program-ming (CoP) formulations for the Constrained FractionalQuadratic Problem (CFQP) and Standard FractionalQuadratic Problem (StFQP) are introduced. Dual andPrimal attainability are discussed. Semidefinite Program-ming (SDP) formulations are proposed for finding goodlower bounds to these fractional programs. A global opti-mization branch-and-bound approach is proposed for theStFQP. Applications of the CFQP and StFQP, related withthe correction of nfeasible linear systems and eigenvaluecomplementarity problems are also discussed.

Paula AmaralUniversidade Nova de [email protected]


Joaquim JudiceUniversidade de [email protected]

MS44

Some New Results in Copositive Programming

We will present some new results concerning the cones ofcopositive and completely positive matrices which play animportant role in quadratic and binary optimization.

Mirjam DuerTU [email protected]

MS44

Testing Copositivity with the Help of Difference-of-Convex Optimization

In this joint work with Mirjam Duer, we consider the prob-lem of minimizing an indefinite quadratic function overthe nonnegative orthant, or equivalently, the problem ofdeciding whether a symmetric matrix is copositive. Weformulate the problem as a difference-of-convex functions(d.c.) problem. Using an appropriate conjugate duality, weshow that there is a one-to-one correspondence betweentheir respective stationary points and minima. We thenapply a subgradient algorithm to approximate those sta-tionary points and obtain an efficient heuristic to verifynon-copositivity of a matrix. Keywords: Copositive matri-ces; difference-of-convex functions(d.c.); Legendre-Fencheltransforms; nonconvex duality; subgradient algorithms ford.c.functions.

Jean-Baptiste Hiriart-Urruty

University of [email protected]

MS44

Accelerated Projection Methods for SemidefinitePrograms

Accelerated projection methods are particularly suitablefor optimization problems over the intersection of thesemidefinite cone and the nonnegative cone or other poly-hedral cones of sparse structure such as triangle inequali-ties. We present a simple algorithm and numerical resultsfor the Lovasz-Schrijver θ-number of graphs with up to1000 vertices.

Florian JarreMathematisches InstitutUniversitaet Duesseldorf, [email protected]

Thomas DaviUniversitaet Duesseldorf, GermanyMathematisches [email protected]

MS45

Dynamic Markets as Differential Variational In-equalities

We investigate the effects of the physical layer of the energyinfrastructure on the behavior of energy markets. We usedifferential variational inequalities as a flexible frameworkin which to describe both the market and physical lay-ers. We investigate the effects of the various market designstrategies and on the overall stability of the closed-loop sys-tem. We discuss the computational cost of the strategies ofdecision-makers and approximations that make them suit-able for real-time environments.

Mihai AnitescuArgonne National LaboratoryMathematics and Computer Science [email protected]

Victor ZavalaArgonne National [email protected]

MS45

Differential Variational Inequalities in Control

It is well-known that checking certain controllability prop-erties of very simple piecewise linear systems are undecid-able problems. This paper deals with the controllabilityproblem of a class of piecewise linear systems, known aslinear complementarity systems. By exploiting the under-lying structure and employing the results on the controlla-bility of the so-called conewise linear systems, we present aset of inequality type conditions as necessary and sufficientconditions for controllability of linear complementarity sys-tems. The presented conditions are of PopovBelevitch-Hautus type in nature.

Kanat CamlibelUniversity of GroningenInstitute of Mathematics and Computer [email protected]

132 OP11 Abstracts

MS45

A Unified Numerical Scheme for Linear-QuadraticOptimal Control Problems with Joint Control andState Constraints

We present a numerical scheme for the convex linear-quadratic optimal control problem with mixed polyhedralstate-control constraints. Unifying the technique of modelpredictive control and a time-stepping method based on thedifferential variational inequality reformulation, the schemesolves a sequence of finite-dimensional problems whose op-timal solutions are employed to construct a discrete-timetrajectory. Such a numerical trajectory is shown to con-verge to an optimal trajectory of the continuous-time prob-lem.

Jong-Shi PangUniversity of Illinois at [email protected]

MS45

Runge-Kutta Methods for Solving DifferentialVariational Inequalities (DVIs)

Runge-Kutta methods can be used for DVIs as they can beused for differential inclusions (see Taubert (1976, 1981),Kastner-Maresch (1990), Dontchev & Lempio (1992)).However, some issues arise in the DVI setting that com-plicate the proofs and results. Under conditions known toimply uniqueness of solutions for the DVI, provided theexact solution is smooth on a given time interval, it canbe shown that the numerical solutions from certain Runge-Kutta methods have the appropriate orders of convergence.Included in these methods is the Radau IIA family of meth-ods which can give arbitrarily high order of convergence.

David E. StewartUniversity of IowaDepartment of [email protected]

MS46

Fast Mixed-integer Model-predictive Control

We present work on nonlinear model predictive controlproblems. In this problem class, some control functionssuch as gear choices may only take values from a discreteset. Based on an Outer Convexification, on Bock’s directmultiple shooting method, and on real-time iterations byDiehl, Bock, and Schloder we present a new mixed-integerreal time iteration scheme and discuss theoretical and al-gorithmic aspects.

Christian KirchesInterdisciplinary Center for Scientific ComputingUniversity of Heidelberg, [email protected]

Sebastian SagerInterdisciplinary Center for Scientific [email protected]

MS46

Computational Complexity Certificates for MPCBased on the Fast Gradient Method

MPC requires the solution of a constrained finite hori-

zon optimal control problem in a receding horizon fashion.Consequently, the solution to this optimization problemhas to be obtained within one sampling period of the con-trol loop. But guaranteeing deterministic termination ofiterative solution methods is a challenging problem in gen-eral. This talk focuses on certifying Nesterov’s fast gradientmethod for constrained linear quadratic MPC and pointsout links between problem data and convergence speed.

Stefan RichterInstitut fur AutomatikETH [email protected]

Colin Jones, Manfred MorariInstitut fur AutomatikETH Zurich, [email protected], [email protected]

MS46

Fast Explicit Nonlinear MPC via MultiresolutionInterpolet Approximation

An algorithm for nonlinear explicit model predictive con-trol is introduced based on multiresolution function ap-proximation that returns a low complexity approximatereceding horizon control law built on a hierarchy of sec-ond order interpolets. Feasibility and stability guaranteesfor the approximate control law are given using reachabilityanalysis. A constructive algorithm is provided that resultsin a control law that is built on a grid hierarchy that is fastto evaluate in real-time systems.

Sean Summers, Davide Raimondo, Colin Jones, JohnLygeros, Manfred MorariInstitut fur AutomatikETH Zurich, [email protected],[email protected], [email protected],[email protected], [email protected]

MS46

Multilevel Iteration Schemes for Nonlinear ModelPredictive Control

Although nonlinear model predictive control has seen manytheoretical and computational advances, the application tosystems requiring fast feedback is still a major computa-tional challenge. In this contribution, we investigate newmulti-level iteration schemes, which distribute the compu-tations occurring in SQP iterations among up to four in-dependent levels, ranging from fast feedback on the lowestlevel, where small QPs are solved very quickly, to completederivative information generation on the topmost level. Wegive details on the implementation and we apply the multi-level iteration schemes to some test problems.

Leonard Wirsching

Interdisciplinary Center for Scientific Computing (IWR)Heidelberg [email protected]


Johannes SchloederIWR, University of Heidelberg, [email protected]

OP11 Abstracts 133

MS47

On Convergence in Mixed Integer Programming

We define the integral lattice-free closure L(P ) of a ratio-nal polyhedron P as the set obtained from P by addingall inequalities obtained from disjunctions associated withintegral lattice-free sets. We show that L(P ) is again apolyhedron, and that repeatedly taking the integral lattice-free closure of P gives its mixed integer hull after a finitenumber of iterations.

Alberto Del [email protected]

MS47

Crooked Cross Cuts for Mixed Integer Programs

We describe a family of asymmetric disjunctive cuts calledcrooked cross cuts. These cuts subsume two dimensionallattice-free cuts and they give the convex hull of mixed-integer programs with two integer variables (and manyconstraints). We also present separation heuristics andencouraging computational results on standard test sets.Joint work with Sanjeeb Dash, Santanu Dey and Juan-Pablo Vielma.

Oktay GunlukIBM, Watson, New [email protected]

MS47

Intersection Cuts with Infinite Split Rank

We consider a mixed integer linear programs where m freeinteger variables are expressed in terms of nonnegative con-tinuous variables. When m = 2, Dey and Louveaux char-acterized the intersection cuts that have infinite split rank.We show that, for any m ≥ 2, the split rank of an intersec-tion cut generated from a bounded convex set P is finite ifand only if the integer points on the boundary of P satisfya certain “2-hyperplane property’.

Amitabh BasuDept. of MathematicsUniversiity of California, [email protected]

Gerard CornuejolsTepper School of BusinessCarnegie Mellon [email protected]

Francois MargotCarnegie Mellon UniversityTepper School of [email protected]

MS48

Detecting Structures in Matrices

Permuting matrices into particular structures, like double-bordered block-diagonal or staircase forms is an area ofinterest in e.g., numerical linear algebra for preparing amatrix for parallel processing. The topic is also interest-ing when it comes to applying decomposition algorithms inlinear and integer programming. As there is a canonical re-lationship between matrices and (hyper-)graphs, we study

some of the structure detection problems on the graphtheoretic side, formulate optimization problems for find-ing ”best” structures, and discuss their usefulness for thementioned decomposition algorithms.

Marco Lubbecke, Martin BergnerRWTH, Aachen [email protected], [email protected]

MS48

Network Design with a Set of Traffic Matrices

A crucial assumption in many network design problemsis that we are given a single matrix of traffic demands(and that is known in advance). Unfortunately, in sev-eral applications, communication patterns among termi-nals change over time, and therefore we are given a set Dof non-simultaneous traffic matrices. Still, we would liketo design a min-cost network that is able to support anytraffic matrix that is from D. In this paper, we discussstrategies for approaching this problem when D is a finiteset. We settle a few complexity questions, present someapproximation based results, and in some cases give exactpolynomial-time algorithms.

Gianpaolo OrioloUniversita di Tor [email protected]

Laura Sanita’Ecole Polytechnique Federale de [email protected]

Rico ZenklusenEPFL [email protected]

MS48

Steiner Tree Approximation Via Iterative Random-ized Rounding

The Steiner tree problem is one of the most fundamen-tal NP-hard problems: given a weighted undirected graphG=(V,E) and a subset of terminal nodes, find a minimumweight tree spanning the terminals. In this talk, we intro-duce a directed LP relaxation and describe an approxima-tion algorithm based on iterative randomized rounding of afractional solution. We prove an approximation guaranteeof 1.39 for the algorithm (improving over the previouslybest known factor of 1.55) and show that the mentionedLP has an integrality gap of at most 1.55 (improving overthe previously best known factor of 2). This is joint workwith Jaroslaw Byrka, Fabrizio Grandoni and Laura Sanita.

Thomas RothvossEPF [email protected]

MS48

Scheduling and Power Assignments in the PhysicalModel for Wireless Networks

In the interference scheduling problem, one is given a set ofn communication requests each of which corresponds to asender and a receiver in a multipoint radio network. Eachrequest must be assigned a power level and a color such

134 OP11 Abstracts

that signals in each color class can be transmitted simul-taneously. The feasibility of simultaneous communicationwithin a color class is defined in terms of the signal to inter-ference plus noise ratio (SINR) that compares the strengthof a signal at a receiver to the sum of the strengths ofother signals. This is commonly referred to as the physicalmodel and is the established way of modeling interferencein the engineering community. The objective is to mini-mize the schedule length corresponding to the number ofcolors needed to schedule all requests. We study obliviouspower assignments in which the power value of a requestonly depends on the path loss between the sender and thereceiver, e.g., in a linear fashion. At first, we present a mea-sure of interference giving lower bounds for the schedulelength with respect to linear and other power assignments.Based on this measure, we devise distributed schedulingalgorithms for the linear power assignment achieving theminimal schedule length up to small factors. In addition,we study a power assignment in which the signal strengthis set to the square root of the path loss. We show thatthis power assignment leads to improved approximationguarantees in two kinds of problem instances defined bydirected and bidirectional communication request. Finally,we study the limitations of oblivious power assignments byproving lower bounds for this class of algorithms.

Berthold VockingRWTH Aachen [email protected]

MS49

On a Problem of Optimal Control of MagneticFields

A problem of optimal magnetization is considered. It isrelated to the time-optimal switching between magneticfields and leads to the minimization of a tracking type func-tional subject to a system of parabolic equations of differ-ential algebraic type. We discuss the sensitivity analysisand present 3D numerical results for a slightly simplifiedgeometry.

Kristof AltmannTechnische Universitaet BerlinInstitut fuer [email protected]

Fredi TroeltzschTechn. University of BerlinDepartment of [email protected]

MS49

Error Estimates for an Optimal Control Problemwith a Non Differentiable Cost Functional

In this talk, semilinear elliptic optimal control problemsinvolving the L1 norm of the control in the objective areconsidered. Necessary and sufficient second-order optimal-ity conditions are derived. A priori finite element error es-timates for piecewise constant discretizations for the con-trol and piecewise linear discretizations of the state areshown. Error estimates for the variational discretizationof the problem, as introduced by Hinze (2005), are alsoobtained. Finally, numerical experiments confirm the con-vergence rates.

Eduardo CasasUniversidad de Cantabria

ETSI Ind y de [email protected]

Roland HerzogChemnitz University of [email protected]

Gerd WachsmuthTU ChemnitzFakultat fur [email protected]

MS49

Bang Bang Control of Elliptic PDEs

In this talk we describe the use of variational approach inorder to discretize elliptic optimal control problems withbang-bang controls. We prove error estimates for the re-sulting scheme and present a numerical example which sup-ports our analytical findings.

Nikolaus von DanielsUniversitat HamburgFachbereich [email protected]

Klaus DeckelnickOtto-von-Guericke-University [email protected]

Michael HinzeUniversitat HamburgDepartment [email protected]

MS49

A Priori Error Analysis of the Petrov GalerkinCrank Nicolson Scheme for Parabolic OptimalControl Problems

In this talk, a finite element discretization of an optimalcontrol problem governed by the heat equation is consid-ered. The temporal discretization is based on a PetrovGalerkin variant of the Crank Nicolson scheme, whereasthe spatial discretization employs usual conforming finiteelements. With a suitable post-processing step, a discretesolution is obtained for which error estimates of optimalorder are proven. A numerical result is presented for illus-trating the theoretical findings.

Boris Vexler, Dominik MeidnerTechnische Universitaet MuenchenCentre for Mathematical Sciences, [email protected], [email protected]

MS50

SQP Methods for Large-scale NLP

Recent advances in MINLP and the solution of NLPs withdifferential equation constraints have revived interest inmethods that may be warm started from a good estimateof a solution. In this context, we review some recent devel-opments in methods for large-scale convex and nonconvexquadratic programming and consider the use of these meth-ods in a sequential quadratic programming (SQP) methodthat exploits both first and second derivatives of the ob-

OP11 Abstracts 135

jective and constraint functions.

Philip E. Gill, Elizabeth WongUniversity of California, San DiegoDepartment of [email protected], [email protected]

MS50

Preconditioners for Matrix-free Interior PointMethod

A new variant of Interior Point Method (IPM) will beaddressed which allows for a matrix-free implementation.Preconditioner(s) suitable in this context will be presentedand their spectral properties will be analysed. The perfor-mance of the method will be illustrated by computationalresults obtained for very large scale optimization problems.This work is an extension of the paper available from:http://www.maths.ed.ac.uk/~gondzio/reports/mtxFree.html.

Jacek GondzioThe University of Edinburgh, United [email protected]

MS50

CQP: a Fortran 90 Module for Large-Scale ConvexQuadratic Programming

We describe the design of a new software package CQP forlarge-scale convex quadratic programming. The methodis based on high-order Taylor and Puiseux approximationto a variety of infeasible arcs connecting the current iter-ate to a better target point. Possible arcs include thoseby Zhang and by Zhou and Sun based on work by Stoer,Mizuno, Potra and others. The resulting algorithm is prov-ably both globally and polynomially convergent at an ul-timately high-order (depending on the series used) in bothnon-degenerate and degenerate cases. We will illustrate anumber of algorithmic options on the CUTEr QP test set.CQP is available as part of the fortran 90 library GALA-HAD.


Dominique OrbanEcole Polytechnique de [email protected]

Daniel RobinsonOxford [email protected]

MS50

A Regularized Primal-Dual SQP Method

We present a regularized SQP method based on a primal-dual augmented Lagrangian function. Trial steps are com-puted from carefully chosen subproblems that utilize re-lationships between traditional SQP, stabilized SQP, andthe augmented Lagrangian. Each subproblem is well de-fined regardless of the rank of the Jacobian, and (to someextent) we challenge the belief that large penalty parame-ters should be avoided. Numerical results on equality con-strained problems from the CUTEr test set are provided.

Daniel RobinsonOxford [email protected]

Philip E. GillUniversity of California, San DiegoDepartment of [email protected]

MS52

Integer Optimization Methods for Ranking Prob-lems in Machine Learning

In supervised ranking, the goal is to optimize a ”rankstatistic,” which measures the quality of a ranked list. Wepresent novel mixed integer programming (MIP) formula-tions for a wide variety of supervised ranking tasks. Otherranking methods use convex functions to approximate rankstatistics in order to accommodate extremely large prob-lems. In contrast, our MIP approach provides exact mod-eling. We report computational results that demonstratesignificant advantages for MIP methods over current state-of-the-art.

Dimitris Bertsimas, Allison ChangMassachusetts Insitute of [email protected], [email protected]

Cynthia RudinMassachusetts Institute of [email protected]

MS52

Learning to Rank with a Preference Function

We discuss novel algorithmic solutions to the problem oflearning to rank in the preference-based setting. Thisformulation of the ranking problem is important since itclosely models that of search engines. Its crucial advan-tage is that it does not require the learning algorithm toreturn a linear ordering of all the points, which may beimpossible to achieve faultlessly with a preference functionin general non-transitive.

Mehryar MohriCourant Institute of Mathematical Sciences & [email protected]

MS52

Label Ranking through Soft Projections onto Poly-hedra

In the talk we focus on the problem of learning to ranklabels from a real valued feedback associated with each la-bel. We cast the feedback as a preferences graph wherethe nodes of the graph are the labels and edges expresspreferences over labels. We tackle the learning problem bydefining a loss function for comparing a predicted graphwith a feedback graph. This loss is materialized by decom-posing the feedback graph into bipartite sub-graphs. Wethen adopt the maximum-margin framework which leads toa quadratic optimization problem with linear constraints.While the size of the problem grows quadratically with thenumber of the nodes in the feedback graph, we derive aproblem of a significantly smaller size and prove that it at-

136 OP11 Abstracts

tains the same minimum. We then describe an efficient al-gorithm, called SOPOPO, for solving the reduced problemby employing a soft projection onto the polyhedron definedby a reduced set of constraints. We also describe and ana-lyze a wrapper procedure for batch learning when multiplegraphs are provided for training. We conclude with thedescription of experiments and applications that demon-strate the merits of SOPOPO. Based on joint work withShai Shalev-Shwartz and Samy Bengio. For more detailsand code see http://www.magicbroom.info/Research.html

Yoram SingerGoogle [email protected]

MS52

Ranking by Pairwise Comparison: Choice ofMethod can Produce Arbitrarily Different RankOrder

For the three methods Principal Eigenvector, HodgeRankand Tropical Eigenvector for obtaining cardinal rankingfrom a paired comparison matrix, we proved the following:for all n > 3, for any rank order pair (σ1, σ2), there ex-ists a comparison matrix in which one method gives theranking σ1, and another method gives the ranking σ2. Wediscuss the implications of this result in practice, study thegeometry of the methods, and state some open problems.

Ngoc Mai TranUniversity of California, [email protected]

MS53

Hyperspectral Data Unmixing using CompressiveSensing—Method and Real-Data Simulations

Hyperspectral data unmixing typically demands enormouscomputational resources in terms of storage, computationand I/O throughputs, especially for real-time processing.In light of the emerging field compressive sensing, we in-vestigate a low complexity scheme for hyperspectral dataacquisition and reconstruction. Specifically, compressedhyperspectral data are acquired directly by a device sim-ilar to the single-pixel camera. Instead of firstly collect-ing the pixels/voxels, it acquires the random projectionsof a scene based on the principle of compressive sensing.To decode the compressed data, we propose a numericalprocedure to straightly compute the unmixed abundancefractions of given endmembers, completely bypassing high-complexity tasks involving the hyperspectral data cube it-self. Grounded on the former work of splitting idea andTVAL3 algorithm, an augmented Lagrangian type algo-rithm is developed to solve the unmixing model. In prac-tice, either the observed data or the priori info may containdisturbance or noise, which causes the trouble of unmix-ing. Experimental and computational results show thatthe proposed scheme has a high potential in real-world ap-plications, even if the noise exists.

Chengbo C. LiRice UniversityDept of Comp and Applied [email protected]

MS53

A Simple and Efficient SVD Algorithm for Princi-

pal Component Analysis

Many data-related applications utilize principal componentanalysis and/or data dimension reduction techniques thatrequire efficiently computing leading parts of singular valuedecompositions (SVD) of very large matrices. In this talk,we introduce a subspace iteration scheme that uses limitedmemory Krylov subspace optimization to do acceleration.We present extensive numerical results comparing a Matlabimplementation of the algorithm with state-of-the-art SVDsolvers. Our tests indicate that the proposed method canprovide better performance under the Matlab environmentover a wide range of problems.

Xin LiuCAAMRICE [email protected]

MS53

Feasible Methods for Optimization with Orthogo-nality Constraints: Part II

We extended the gradient approaches for minimizationwith orthogonality constraints from two perspectives.First, a limited-memory BFGS method is proposed withoutusing the expensive parallel translation or vector transport.Second, in order to handle general constraints, we embedthe orthogonality constraint preserving approaches in theaugmented Lagrangian framework. Numerical experimentson a variety of problems are presented.

Zaiwen WenShanghai Jiao Tong UniversityDepartment of [email protected]

MS53

Feasible Methods For Optimization with Orthogo-nality Constraints: Part I

Minimization with orthogonality constraints (e.g., X�X =I) and/or spherical constraints (e.g., ‖x‖2 = 1) has wideapplications in polynomial optimization, combinatorial op-timization, eigenvalue problems, matrix rank minimiza-tion, etc. To deal with these difficulties, we propose touse a Crank-Nicolson-like update scheme to preserve theconstraints and, based on it, develop a curvilinear searchalgorithm. Preliminary numerical experiments on a widecollection of problems show that the proposed algorithm isvery promising.

Wotao YinRice [email protected]

MS54

Implementation of a Predictive Controller on anFPGA

Predictive control is an advanced control technique thatrelies on the solution of a convex QP at every sample in-stant. In order to apply predictive control at faster sam-pling rates, there is a need for faster methods for solving theoptimization problems. We present an FPGA implementa-tion of an interior-point solver, which provides substantialacceleration over a sequential CPU implementation. In ad-dition, the proposed architecture possesses special featuresthat increase the potential performance benefit by an extra

OP11 Abstracts 137

order of magnitude.

Juan L. Jerez, George Constantinides, Eric C. KerriganImperial College [email protected],[email protected],[email protected]

MS54

A Well-conditioned Interior Point Method with anApplication to Optimal Control

We propose an approximate method for computing thesearch direction at each iteration of an interior pointmethod. If the ratio of the slack variable and dual variableassociated with a constraint is above a given threshold,the KKT system is modified in an appropriately-definedway. We show that the condition number of the KKT ma-trix is improved and that the method performs favorably,compared to existing methods, when solving constrainedoptimal control problems.

Amir Shahzad, Eric C. Kerrigan, George ConstantinidesImperial College [email protected], [email protected],[email protected]

MS54

Multiple Shooting for Large-Scale Systems

We propose a variant of the standard multiple shootingmethod which takes into account the structure of certainlarge-scale systems in order to obtain a better controllerdesign flexibility and high parallelizability. We solve large-scale optimal control problems by making use of adjoint-based sequential quadratic programming. A numerical ex-periment shows that this can lead to considerable savingsin computational time for the sensitivity generation.

Carlo Savorgnan, Attila KozmaDepartment of Electrical EngineeringKU Leuven, [email protected],[email protected]

Joel AnderssonElectrical Engineering [email protected]


MS54

Distributed Optimization Methods for Large -Scale Control Problems

In this paper we analyze the optimization-theoretic con-cepts of parallel and distributed methods for solving large-scale coupled optimization problems and demonstrate howseveral estimation and control problems related to complexnetwork systems can be formulated in these settings. Thepaper presents a systematic framework to exploit the po-tential of the decomposition structures as a way to obtaindifferent parallel algorithms, each with a different tradeoffamong convergence speed, message passing amount, and

distributed computation architecture.

Ion Necoara, Ioan Dumitrache, Valentin NedelcuUniversity Politehnica [email protected], [email protected],[email protected]

MS55

Warmstarting Interior-Point Methods for SDP inthe Cutting-Plane Method

We present our recent progress with warmstarting succes-sive SDP relaxations in cutting-plane schemes for combina-torial optimization problems. Following previous advancesof interior-point warmstarts for LP, we show how to gen-eralize such strategies for SDP and explore their computa-tional promise and effectiveness. We also plan to addressthe problem of warmstarting SDP after data perturbationsand propose a set of test problems to be used as warmstart-ing benchmarks.

Alexander EngauUniversity of Colorado, Denver, [email protected]

MS55

Warmstaring Interior Point Strategies for Combi-natorial Optimization Applications

When solving a sequence of closely-related problems,warmstaring strategies are essential. In recent years sev-eral of these techniques have been proposed for interiorpoint methods. In this talk, we present some of these tech-niques and propose new warmstarting strategies applicablein a column generation framework. We compare them withother strategies in the literature when solving combinato-rial optimization problems. Our preliminary results sug-gest that an efficient warmstarting strategy offers savingsin both, time and iterations.

Pablo Gonzalez-BrevisSchool of [email protected]


MS55

Approximate Solutions of SDP Relaxations

Interior point methods for semidefinite programs are lim-ited in the size of instances they can solve, so many alter-native approaches have been developed. These may leadto solutions that satisfy the positive semidefiniteness re-quirement only in the limit. Randomization techniques areoften applied to the SDP solution to provide a solution toan underlying problem. We quantify the effect of solvingthe SDP approximately on the quality of the randomizedsolution for some problem classes.

Tim LeeDept of Mathematical SciencesRensselaer Polytechnic [email protected]

John E. MitchellRensselaer Polytechnic Institute

138 OP11 Abstracts

110, 8th Street, Troy, NY, [email protected]

MS55

Solving Combinatorial Optimization Problemswith Interior Point Methods

A wealth of solution methods is available for solving com-binatorial optimization problems. Focusing on general-purpose exact methods based on integer programmingmodels, the standard approaches rely on solving a sequenceof closely related linear programming problems. In thistalk, we address the challenging issues of using a primal-dual interior point method within a branch-and-price-and-cut strategy, and present preliminary computational resultsfor classical combinatorial optimization problems from theliterature.

Pedro MunariUniversity of Sao Paulo, [email protected]


MS56

A Parallel Framework for Identifying Vulnerabili-ties in the Electric Power Grid

Identifying multiple contingencies of an electric power gridrequires the solution of a large bilevel optimization prob-lem, which is computationally expensive. We explore aparallel branch-and-bound framework that exploits the dis-creteness of the outer-level variables instead of relaxingthem to continuous ones. The framework is nicely decou-pled in the sense that it allows various optimal power flow(OPF) algorithms to be used for the inner-level load shed-ding problem. We evaluate our framework on a real-sizedproblem.

Juan C. MezaLawrence Berkeley National [email protected]

Aydin BulucLawrence Berkeley [email protected]

MS56

MOPEC Models for Energy Problems

We consider MOPEC models: collections of optimizationproblems linked by equilibrium (or complementarity) con-straints. We show the relevance of this modeling frameworkto a number of different problems associated with energyplanning, and detail several algorithms for their solution.The model will incorporate stochastic effects, contracts,and the possibility of retention of goods.

Michael C. FerrisUniversity of WisconsinDepartment of Computer [email protected]

Roger WetsUniversity of California, [email protected]

MS56

Optimal Design of System Architectures

Design of large complex systems (e.g. buildings, dis-tributed power systems, transportation networks, etc.) hasbeen challenging due to the huge design space, non-lineardiscontinuous dynamic behavior, and uncertainties opera-tional scenarios unknown during the design phase. Theseproblems fall in the class of non-convex mixed integer non-linear programs which is an active area of research. In thistalk, we will present a two phase optimization approach -Comprehensive Screening (CS) and High Fidelity Evalua-tion (HFE) for the optimal design of large systems withspecific application to microgrid architectures. In the CSphase, a mixed integer linear program (MILP) representa-tion is used to mathematically capture the space of designalternatives. Key to this is the assumption of linear mod-els for the components in the system. The HF phase usesthe optimal architecture and nonlinear model for the com-ponents to determine the optimal sizing and dispatchingdecisions. In this talk, we will overview the methodologywhen applied to the design of energy supply systems thatwould minimize lifecycle costs while meeting a given electri-cal and thermal demand pattern. We will also investigateapproaches for including uncertainty in input variables.

Arvind Raghunathan, Niranjan Desai, Ritesh Khire,Stella Oggianu, Xin Wu, Shui Yuan, Larry ZeidnerUnited Technologies Research [email protected], [email protected],[email protected], [email protected],[email protected], [email protected],[email protected]

MS56

Title: Multi-stage Stochastic Decomposition withApplications in Energy Systems Planning

Many energy systems planning require that they be inte-grated with simulators that are capable of providing sam-ple paths over hours, and sometimes days. However, moststochastic programming algorithms are designed to use acollection of scenarios rather than working with samplepaths, one at a time. We will discuss a multi-stage versionof Stochastic Decomposition which allows us to integrateoutputs from a simulator directly into the planning model.Applications in power system planning and operations willbe discussed.

Suvrajeet SenIntegrated Systems EngOhio State [email protected]

MS57

Identification of an Unknown Parameter in theMain Part of an Elliptic PDE

Identification of an Unknown Parameter in the Main Partof an Elliptic PDE We are interested in identifying an un-known material parameter a(x) in the main part of an el-liptic partial differential equation

−div (a(x) grad y(x)) = g(x) in Ω

with corresponding boundary conditions. We discuss a Ti-chonov regularization

mina

J(y, a) = ‖y − yd‖2L2(Ω) + α‖a‖2

Hs(Ω)

OP11 Abstracts 139

with s > 0. Moreover, we require the following constraintsfor the unknown parameter

0 < amin ≤ a(x) ≤ amax.

The talk starts with results on existence of solutions andnecessary optimality conditions. The main part of the talkwill be devoted to sufficient optimality conditions.

Arnd Rosch, Ute AßmannUniversity of [email protected], [email protected]

MS57

Optimal Control of PDEs with Directional Sparsity

We study optimal control problems in which controls withcertain sparsity patterns are preferred. For time-dependentproblems the approach can be used to find locations forcontrol devices that allow controlling the system in an op-timal way over the entire time interval. The approach useson a non-differentiable cost functional to implement thesparsity requirements; additionally, bound constraints forthe optimal controls can be included. We study the re-sulting problem in appropriate function spaces and presenttwo solution methods of Newton type, based on differentformulations of the optimality system. Using elliptic andparabolic test problems we research the sparsity propertiesof the optimal controls and analyze the behavior of theproposed solution algorithms.

Gerd WachsmuthTU ChemnitzFakultat fur [email protected]

MS57

Adaptive Discretization Strategies for ParameterIdentification Problems in PDEs in the Context ofTikhonov Type and Newton Type Regularization

Parameter identification problems for PDEs often lead tolarge scale inverse problems. To reduce the computationaleffort for the repeated solution of the forward and even ofthe inverse problem as it is required for determining theregulrization parameter according to the discrepancy prin-ciple in Tikhonov regularization we use an adaptive dis-cretization based on goal oriented error estimators. Thisconcept originating from optimal control provides an esti-mate of the error in a so-called quantity of interest a func-tional of the control q (which in our context is the searchedfor parameter) and the PDE solution u based on whichthe discretizations of q, u (and possibly also the adjointPDE solution) are locally refined. The crucial question forparameter identification problems is now the choice of anappropriate quantity of interest. A convergence analysis ofthe Tikhonov regularization with the discrepancy principleon discretized spaces for q and u shows, that in order todetermine the correct regularization parameter, one has toguarantee sufficiently high accuracy in the squared residualnorm which is therefore our quantity i of interest whereasq and u themselves need not be computed precisely ev-erywhere. This fact allows for relatively low dimensionaladaptive meshes and hence for a considerable reduction ofthe computational effort. Alternatively to Tikhonov regu-larization we consider Newton type regularization methodsand their adaptive discretization, again based on a goaloriented approach. Numerical tests will illustrate the effi-

ciency oft he proposed methods.

Barbara kaltenbacherUniversity of GrazInstitute for Mathematics and Scientific [email protected]

MS58

Deciding Polynomial Convexity Is NP-hard

We show that unless P=NP, there exists no polynomialtime (or even pseudo-polynomial time) algorithm that candecide whether a multivariate polynomial of degree four(or higher even degree) is globally convex. This solves aproblem that has been open since 1992 when N. Z. Shorasked for the complexity of deciding convexity for quarticpolynomials. We also prove that deciding strict convex-ity, strong convexity, quasiconvexity, and pseudoconvexityof polynomials of even degree four or higher is stronglyNP-hard. By contrast, we show that quasiconvexity andpseudoconvexity of odd degree polynomials can be decidedin polynomial time.

Amir Ali Ahmadi, Alex Olshevsky, Pablo A. ParriloMITa a [email protected], alex [email protected], [email protected]

John N. TsitsiklisMassachusetts Institute of [email protected]

MS58

Positive Polynomials on Equality-Constrained Do-mains

We establish a simple connection between the set of polyno-mials that are non-negative on a given domain and the setof polynomials that are non-negative on the intersectionof the same domain and the zero of a given polynomial.This connection has interesting algorithmic implications.For instance, it readily yields a succinct derivation of acopositive programming formulation for quadratically con-strained quadratic programs.

Javier PenaCarnegie Mellon [email protected]

MS58

Dynamic Generation of Valid Polynomial Inequal-ities for Polynomial Programs

Recently semidefinite programs have been used to buildhierarchies of convex relaxations to polynomial programs.This approach is computationally expensive and is onlytractable for small problems. We propose an algorithmto dynamically generate valid polynomial inequalities togeneral polynomial programs. When use iteratively thisalgorithm solves a cheap ”master relaxation” - ”inequal-ity generating subproblem” pair to improve the relaxationof the original problem, obtaining better bounds for theoptimal value. We present results on non-convex binaryquadratic problems to illustrate the effectiveness of thisapproach.

Juan C. VeraTilburg UniversityDepartment of Econometrics and Operations [email protected]

140 OP11 Abstracts

Bissan GhaddarUniversity of [email protected]

Miguel F. AnjosMathematics and Industrial Engineering & GERAD

Ecole Polytechnique de [email protected]

MS58

Computing General Static-arbitrage Bounds forEuropean Basket Options via Dantzig-Wolfe De-composition

We study the problem of computing general static-arbitrage bounds for European basket options; that is,computing bounds on the price of a basket option, giventhe only assumption of absence of arbitrage, and informa-tion about prices of other European basket options on thesame underlying assets and with the same maturity. Inparticular, we provide a simple efficient way to computethis type of bounds by solving a large finite non-linear pro-gramming formulation of the problem. This is done viaa suitable Dantzig-Wolfe decomposition that takes advan-tage of an integer programming formulation of the corre-sponding subproblems.Our computation method equally applies to both up-per and lower arbitrage bounds, and provides a solutionmethod for general instances of the problem. This con-stitutes a substantial contribution to the related litera-ture, in which upper and lower bound problems need tobe treated differently, and which provides efficient ways tosolve particular static-arbitrage bounds for European bas-ket options; namely, when the option prices informationused to compute the bounds is limited to vanilla and/orforward options, or when the number of underlying assetsis limited to two assets.Also, our computation method allows the inclusion of real-world characteristics of option prices into the arbitragebounds problem, such as the presence of bid-ask spreads.We illustrate our results by computing upper and lowerarbitrage bounds on gasoline/heating oil crack spread op-tions.

Luis F. ZuluagaUniversity of New [email protected]

Javier PenaCarnegie Mellon [email protected]

Xavier SaynacFaculty of Business AdministrationUniversity of New [email protected]

Juan C. VeraTilburg UniversityDepartment of Econometrics and Operations [email protected]

MS59

Quantifying and Managing Complexity in Trans-port Systems

Growing autonomy and distribution will characterize fu-ture air transportation systems. Managing the ensuing

complexity requires new approaches to quantifying andcontrolling complexity. We investigate techniques aimedat modeling complexity computationally based on nonlin-ear programming formulations, as well as algorithms forhandling complexity from a variety of spatial and tempo-ral perspectives.

Natalia AlexandrovNASA Langley Research [email protected]

MS59

Excursions into Multi-disciplinary Design underUncertainty in Aerospace Engineering

This presentation will discuss the application of design un-der uncertainty techniques within the context of multi-disciplinary aerospace systems. We pay particular atten-tion to both the design of supersonic low-boom aircraft andof hypersonic propulsion systems where multiple disciplines(aerodynamics, acoustics, turbulence, combustion) need tobe considered and where both aleatory and epistemic un-certainties are present. The results of our designs focus onboth robust and reliable outcomes.

Juan J. AlonsoDepartment of Aeronautics and AstronauticsStanford [email protected]

MS59

Evaluation of Mixed Continuous-discrete SurrogateApproaches

Evaluating the performance of surrogate modeling ap-proaches is essential for determining their viability in opti-mization or uncertainty analysis. To this end, we evaluatedcategorical regression, ACOSSO splines, and treed GPs ona set of test functions. We describe the principles andmetrics we used for this evaluation, the characteristics ofthe test functions we considered, and our software testbed.Additionally, we present our numerical results and discussour observations regarding the merits of each approach.

Patricia D. HoughSandia National [email protected]

Laura SwilerSandia National LaboratoriesAlbuquerque, New Mexico [email protected]

Herbie LeeUniversity of California, Santa CruzDept. of Applied Math and [email protected]

MS59

Direct Search Methods for Engineering Optimiza-tion Problems with General Constraints

We investigate the behavior of derivative-free direct searchmethods for nonlinear optimization problems with generalconstraints where either the objective or (some of) the con-straints are defined by complex simulations. Of particularinterest is why derivative-free methods that rely on build-ing direct models of the objective encounter difficulties –

OP11 Abstracts 141

particularly as the number of variables grows – when theconstraints are more than just simple bounds on the vari-ables.

Robert Michael LewisCollege of William & MaryDept. of [email protected]

Virginia J. TorczonCollege of William & MaryDepartment of Computer [email protected]

MS60

Dynamic Sample Size Selection in Algorithms forMachine Learning

When solving large-scale machine learning and stochasticoptimization problems, sample size selection is an impor-tant component to consider, given its influence over bothefficiency and accuracy. Incorporating dynamic samplesizes may also allow an algorithm’s performance to behavemore capably in implementation, in comparison to a staticsample size. The work that will be presented will suggestappropriate methods for dynamically improving the samplesize selection. Both numerical and theoretical complexityresults shall be presented.

Gillian ChinNorthwestern [email protected]

MS60

Spectral Gradient Methods for Nonlinear Pro-gramming

The development of new software for NLP is described.There are two main design aims (i) to avoid the use of sec-ond derivatives, and (ii) to avoid storing an approximatereduced Hessian matrix by using a new limited memoryspectral gradient approach based on Ritz values. The basicapproach to NLP is that of Robinson’s method, globalisedby using a filter and trust region, rather than a squarepenalty term such as in MINOS. A new code for the lin-ear constraint subproblem (LCP) has been developed usingthe Ritz values approach. Numerical experience will be de-scribed.

Roger FletcherUniversity of DundeeDepartment of Mathematics &[email protected]

MS60

New Methods for Regularized Machine Learningand Stochastic Programming

We consider machine learning problems, such as those aris-ing in speech recognition, where the number of trainingpoints can reach into the billions. We describe new on-line and distributed gradient methods capable of solvingproblems of this type. Our methods use regularized logis-tic models that promote sparse parameters. We demon-strate the efficiency of the proposed methods using a pro-duction system at Google. We also present complexity re-sults comparing sequential online methods and mini-batch

distributed gradient methods.

Jorge NocedalDepartment of Electrical and Computer EngineeringNorthwestern [email protected]

Yuchen [email protected]

MS60

Semismooth Newton Methodswith Multi-dimensional Filter Globalization for l1Optimization

The sparsity-promoting properties of l1-regularizationshave many important applications. We present a classof methods for l1-regularized optimization problems thatcombine semismooth Newton algorithms with globally con-vergent descent methods in a flexible way. The accep-tance of semismooth Newton steps is controlled by a multi-dimensional filter, which efficiently relaxes sufficient de-crease requirements for these steps. Global convergence aswell as transition to fast local convergence are investigated.We conclude with numerical illustrations.

Michael UlbrichTechnical University of MunichChair of Mathematical [email protected]

Andre MilzarekTechnische Universitaet MuenchenDepartment of Mathematics, [email protected]

MS62

CasADi - A Tool for Dynamic Optimizationand Automatic Differentiation for Object-orientedModelling Languages

We introduce CasADi, an implementation of automaticdifferentiation in forward and adjoint mode using a hy-brid operator-overloading, source-code-transformation ap-proach. For maximum efficiency, CasADi works with acombination of two different graph representations : Onesupporting only scalar-valued, built-in unary and binaryoperations without branching and secondly, a representa-tion supporting matrix-valued operations, branchings suchas if-statements as well as function calls to arbitrary func-tions (e.g. ODE/DAE integrators).

Joel AnderssonElectrical Engineering [email protected]


MS62

On an Iterative Range Space Method

We present several modifications for the total quasi-Newton method to solve general nonlinear problems. Bythe use of low-rank approximation and automatic differ-

142 OP11 Abstracts

entiation, no exact evaluation of the constraint Jacobianand the Hessian of the Lagrangian is required in this ap-proach. To make the method more suitable for large scaleoptimization we employ a range space factorization usingwell-known limited memory techniques with compact stor-age such as L-BFGS and L-SR1.

Torsten F. BosseHumboldt-Universitat zu Berlin,Institut fur [email protected]

Andreas GriewankHU Berlin, MATHEON Research Center, [email protected]

MS62

Solving Time-Harmonic Inverse Medium Opti-mization Problems with Inexact Interior-PointStep Computation

We formulate an inverse medium problem as a PDE-constrained optimization problem, where the underlyingwave field solves the time-harmonic Helmholtz equation.Ill-posedness is tackled through regularization while theinclusion of inequality constraints is used to encode priorknowledge. The resulting nonconvex optimization problemis solved by a primal-dual interior-point algorithm with in-exact step computation. Numerical results both in twoand three space dimensions illustrate the usefulness of theapproach.

Olaf SchenkDepartment of Mathematics and Computer ScienceUniversity of Basel, [email protected]

Marcus GroteUniversitat [email protected]

Johannes HuberUniversity of [email protected]

Andreas WachterIBM T. J. Watson Research [email protected]

Frank E. CurtisIndustrial and Systems EngineeringLehigh [email protected]

MS62

On an Inexact Trust-region Approach for Inequal-ity Constrained Optimization

This talk presents a trust-region SQP algorithm for the so-lution of minimization problems with nonlinear inequalityconstraints. The approach works only with an approxima-tion of the constraint Jacobian. Hence, it is well suited foroptimization problems of moderate size but with dense con-straint Jacobian. The accuracy requirements for the pre-sented first-order global convergence result can be verifiedeasily during the optimization process. Numerical results

for some test problems are shown

Andrea WaltherUniversitat [email protected]

Lorenz T. BieglerCarnegie Mellon [email protected]

MS63

Small Chvatal Rank

We propose a variant of the Chvatal-Gomory procedurethat will produce a sufficient set of facet normals for theinteger hulls of all polyhedra {x : Ax ≤ b} as b varies.The number of steps needed is called the small Chvatalrank (SCR) of A. We characterize matrices for which SCRis zero via the notion of supernormality which generalizesunimodularity. SCR is studied in the context of the stableset problem in a graph, and we show that many of the well-known facet normals of the stable set polytope appear inat most two rounds of our procedure. Our results reveal auniform hypercyclic structure behind the normals of manycomplicated facet inequalities in the literature for the sta-ble set polytope. Lower bounds for SCR are derived bothin general and for polytopes in the unit cube.

Tristram BogartSan Francisco State [email protected]

Annie RaymondBerlin Mathematical [email protected]

Rekha ThomasUniversity of [email protected]

MS63

Grobner Bases and Hilbert’s Nullstellensatz: Com-binatorial Interpretations and Algorithmic Tech-niques

Systems of polynomial equations with coefficients over analgebraically closed field K can be used to concisely modelcombinatorial problems. In this way, a combinatorial prob-lem is feasible (e.g., a graph is 3-colorable, hamiltonian,etc.) if and only if a related system of polynomial equationshas a solution. We present a collection of results based onthese non-linear models. In the case of the independent setproblem, we present a combinatorial interpretation of theHilbert’s Nullstellensatz certificate of infeasibility. In thecase of the dominating set problem, we present a combi-natorial interpretation of the universal Grobner basis. Inthe case of graph 3-coloring, we demonstrate an algorithmthat is surprisingly practical in practice.

Susan MarguliesComputational and Applied MathematicsRice [email protected]

OP11 Abstracts 143

MS63

The Border Basis Closure

The Sherali-Adams lift-and-project hierarchy is a funda-mental construct in integer programming, which providessuccessively tighter linear programming relaxations of theinteger hull of a polytope. We initiate a new approach tounderstanding the Sherali-Adams procedure by relating itto methods from computational algebraic geometry. Wepresent a modified version of the border basis algorithmto generate a hierarchy of linear programming relaxationsthat are stronger than those of Sherali and Adams, andover which one can still optimize in polynomial time (fora fixed number of rounds in the hierarchy). In contrast tothe well-known Grbner bases approach to integer program-ming, our procedure does not create primal solutions, butconstitutes a novel approach of using computer-algebraicmethods to produce dual bounds.

Sebastian Pokutta, Andreas S. SchulzMassachusetts Institute of [email protected], [email protected]

MS63

Graver Bases Methods in Integer Programming

N-fold integer programming is a fundamental problem witha variety of natural applications in operations research andstatistics. Moreover, it is universal and provides a new,variable-dimension, parametrization of all of integer pro-gramming.We use Graver bases methods to establish aniterative algorithm that solves this problem in polynomialtime. Using it, we also propose a simple Graver approx-imation hierarchy, parameterized by degree, for nonlinearinteger programming in general and optimization over mul-tiway tables in particular, which makes use of quickly con-structible approximations of the true Graver basis. Wedemonstrate this scheme for approximating the (universal)integer three-way table feasibility problem. The talk isbased on joint work with S. Onn, R. Hemmecke and on mythesis in preparation (under the supervision of S. Onn).

Lyubov RomanchukTechnion - Israel Institute of Technology, [email protected]

MS64

On Maximally Violated Cuts Obtained from a Ba-sis

Most cuts used in practice can be derived from a basis andare of the form αT x ≥ 1, where x is a vector of non-basicvariables and α ≥ 0. Such cuts are called maximally vio-lated wrt a point x ≥ 0 if αT x = 0. In an earlier paperwe presented computational results for maximally violatedcuts derived from an optimal basis of the linear relaxation.In this talk we also consider pivoting and deriving maxi-mally violated cuts from alternative non-optimal bases.

Kent AndersenUniversity of [email protected]

Adam N. LetchfordLancaster University Management [email protected]

Robert WeismantelETH Zuerich

[email protected]

MS64

A Verification Based Method to Generate StrongCutting Planes for IPs

A cutting-plane procedure for integer programming (IP)problems usually involves invoking a black-box procedureto compute a cutting plane. In this paper, we describean alternative paradigm of using the same cutting-planeblack-box. This involves two steps. In the first step, wedesign an inequality cx ≤ d, independent of the cuttingplane black-box. In the second step, we verify that the de-signed inequality is a valid inequality by verifying that theset P ∩ {x ∈ Rn : cx ≥ d + 1} ∩ Zn is empty using cuttingplanes from the black-box. (Here P is the feasible regionof the linear-programming relaxation of the IP.) We referto the closure of all cutting planes that can be verified tobe valid using a specific cutting plane black-box as the ver-ification closure of the considered black box. This verifica-tion paradigm naturally leads to the question of how muchextra strength one might hope to gain by having an ora-cle in place that provides us with potential cutting-planesand we are left with the task of verifying that its outputis valid. We show that cutting-plane obtained via the ver-ification scheme can be very strong, significantly exceed-ing the capabilities of the regular cutting-plane procedure.On the other hand, we present lower bounds on the rankof verification cutting planes for known difficult infeasible0/1 instances, showing that while verification procedure isstrong, it is not unrealistically so.

Santanu S. DeyGeorgia Institute of TechnologySchool of Industrial and System [email protected]

Sebastian PukuttaSloan School of Management, [email protected]

MS64

Generating Two-Row Cuts from Lattice-Free Bod-ies

Andersen et al (2007) and Cornuejols and Margot (2009)show that facet-defining inequalities of a system with twoconstraints and two integer variables are related to maxi-mal lattice-free convex sets. We give an algorithm to con-struct those sets, thereby enumerating all facet-defininginequalities for such systems. Computational results arepresented.

Kenneth [email protected]


Ricardo FukasawaUniversity of [email protected]

Daniel [email protected]

144 OP11 Abstracts

MS64

Approximating the Split Closure

The first split closure has been proven in practice to be avery tight approximation of the ideal convex hull formula-tion of a generic Mixed Integer Program (MIP). However,exact separation procedures for optimizing over it have un-acceptable computing times. We present heuristic proce-dures for approximating the split closure of a MIP, as wellas algorithmic techniques for speeding up such separation.Preliminary computational results show the effectivenessof the proposed procedures compared to the state of theart.

Matteo Fischetti, Domenico SalvagninUniversity of [email protected], [email protected]

MS65

Flexible First-order Methods for Rank Minimiza-tion

We describe a flexible framework for solving constrainednon-smooth convex programs, such as nuclear norm mini-mization and LASSO. The technique is based on smooth-ing and solving the dual formulation. An advantage of thetechnique is that it allows for many variations, such as arobust-PCA formulation. We also discuss the special casewhere the solution is known to be PSD, which occurs incovariance estimation and quantum tomography.

Stephen BeckerCalifornia Institute of [email protected]

Ewout van den BergStanford [email protected]

MS65

Fast First-Order and Alternating Direction Meth-ods for Stable Princial Component Pursuit

Given a matrix M that is the sum of a low rank matrixX and a sparse matrix Y, it is known that under certainconditions, X and Y can be recovered with very high prob-ability by solving a so-called robust principal componentpursuit problem. When M has noise added to it, the recov-ery problem is called stable principal component pursuit.In this problem one minimizes the sum of the nuclear normof X plus a scalar times the sum of the absolute values ofthe elements of Y, subject to the Frobenius norm of X+Y-M being less than some known noise level. We show howto apply Nesterov’s optimal gradient and composite meth-ods and a fast alternating linearization method to obtainepsilon-optimal solutions in O(1/epsilon) iterations, whilekeeping the cost of each iteration low. We also propose analternating direction augmented Lagrangian method thatis extremely efficient, for which we prove convergence.

Don Goldfarb, Necdet AybatColumbia [email protected], [email protected]

MS65

A Proximal Point Algorithm for Nuclear Norm

Regularized Matrix Least Squares Problems

We introduce a proximal point algorithm for solving nu-clear norm regularized matrix least squares problems withequality and inequality constraints. The inner subprob-lems are solved by an inexact smoothing Newton method,which is proved to be quadratically convergent under a con-straint non-degenerate condition, together with the strongsemi-smoothness property of the singular value threshold-ing operator. Numerical experiments on problems arisingfrom low-rank approximations of transition matrices showthat our algorithm is efficient and robust.

Kaifeng JiangDepartment of MathematicsNational University of Singapore, [email protected]



MS66

A Bilevel Optimization Approach to Obtaining Op-timal Cost Functions for Human Arm Movements

It is known that human motions are (approximately) op-timal for suitable, unknown cost functions subject to thedynamics. We use bilevel optimization to investigate thefollowing inverse problem: Which cost function out of aparameterized family composed from functions suggestedin the literature reproduces recorded human arm move-ments best? The lower level problem is an optimal controlproblem governed by a nonlinear model of the human armdynamics. Promising applications are also discussed.

Sebastian Albrecht, Marion LeiboldTechnische Universitaet [email protected], [email protected]


MS66

Optimality Conditions for Bilevel Programming

Bilevel programming problems are hierarchical optimiza-tion problems where the feasible region is (in part) re-stricted to the graph of the solution set mapping of a secondparametric optimization problem. To solve them and to de-rive optimality conditions for these problems this paramet-ric optimization problem needs to be replaced with its (nec-essary) optimality conditions. This results in a (one-level)optimization problem. In the talk different approaches totransform the bilevel programming will be suggested andthe relations between the original bilevel problem and theone replacing it will be investigated. The resulting (neces-sary) optimality conditions will be formulated.

Stephan DempeTechnical University of Freiberg

OP11 Abstracts 145

09596 Freiberg, [email protected]

Alain B. ZemkohoInstiut of Numerical Mathematics and OptimizationTU Bergakademie [email protected]

MS66

Mathematical Programs with Vanishing Con-straints

A new class of constrained optimization problems calledmathematical programs with vanishing constraints (MPVC)is considered. This type of problem is known to act as aunified framework for several problems from topology opti-mization and is hence very interesting from an engineeringpoint of view. Moreover, due nonconvexity and violation ofmost of the standard constraint qualifications, an MPVCis very challenging from a theoretical and numerical view-point. In the face of that, problem-tailored constraint qual-ifications and the related stationarity concepts are investi-gated. Moreover, a numerical approach for the solution ofan MPVC is surveyed.

Tim HoheiselUniversity of Wurzburg97074 Wurzburg, [email protected]

MS66

On the Concept of T-stationarity in MPCC andMPVC

We call a stationarity concept for a given class of opti-mization problems topologically relevant, if it allows to es-tablish a Morse theory. Recent results about mathemat-ical programs with vanishing constraints (MPVCs) illus-trated that the topologically relevant stationarity conceptis not necessarily one which is already known, in contrastto finite smooth constrained optimization and MPCCs,where KKT stationarity and C-stationarity are topologi-cally relevant, respectively. This motivated the introduc-tion of T-stationarity for MPVCs. We point out con-nections to numerical methods for MPCCs and MPVCs,where KKT points of smooth approximations tend to T-stationary points of the original problems.

Oliver SteinKarlsruhe Institute of Technology76131 Karlsruhe, [email protected]

MS67

Optimization Applied to Electricity GenerationManagement at EdF

We consider the one-day-ahead scheduling of a power mixwith about 150 thermal plants and 50 hydro-valleys, as toensure offer and demand equilibrium at minimal cost, whilesatisfying the technical constraints of all plants. From theoptimization point-of-view, the problem is quite difficultbecause it must be solved in less than 15 minutes; butit is large-scale, with 106 mixed-integer variables and 106

nonconvex and discontinous constraints. We focus on thelatest developments about the optimisation methods that

are used to solve this problem.

Sandrine CharoussetEDF [email protected]

MS67

The Value of Rolling Horizon Policies for Risk-averse Hydro-thermal Planning

We consider the optimal management of a hydro-thermalpower system in the mid-term. This is a large-scale mul-tistage stochastic linear program, often solved by combin-ing sampling with decomposition algorithms, like stochas-tic dual dynamic programming. However, such method-ologies may entail prohibitive computational time, espe-cially when applied to a risk-averse formulation of the prob-lem. For a model that takes into account losses and un-certainty in both the inflows and the demand, we proposea risk-averse rolling horizon approach based on subprob-lems having deterministic constraints for the current timestep and future uncertain constraints dealt with as chanceand CVaR constraints. When uncertainty in the problemis represented by a periodic autoregressive stochastic pro-cess, each subproblem is a medium-size linear program,easy to solve. Being both nonanticipative and feasible, theresulting risk-averse policy keeps reservoirs above certaincritical levels almost surely. In order to evaluate the ben-efits of the rolling horizon approach, we introduce a non-rolling horizon policy, both robust and feasible, based onsolutions obtained at the first time step with the rollinghorizon methodology. When applied to a real-life powersystem, the superiority of the rolling approach becomesevident, compared both to the non-rolling horizon policyaforementioned and to a stochastic dual dynamic program-ming strategy, frequently employed for this type of prob-lems.

Vincent [email protected]


MS67

The N-k Problem using AC Power Flows

Given a power grid, we search for a set of k or fewer lineswhose simultaneous outage will impact stability. We studythis problem under AC power flows; our concepts of ”sta-bility” primarily focus on voltage stability. In our approachwe bypass combinatorial complexity by positing an intel-ligent adversary who can increase the resistance or reac-tance of power lines, within budgets, so as to maximize theresulting instability. This problem is continuous (thoughnonconcave) and thus, amenable to continuous optimiza-tion techniques. We report on experiments using large,real-world grids.

Sean HarnettColumbia [email protected]

Daniel BienstockColumbia University IEOR and APAM DepartmentsIEOR Department

146 OP11 Abstracts

[email protected]

MS67

Security Constrained Optimization for ElectricPower Systems

The need for improving security standards for electricpower systems is well recognized. Such efforts however,are hindered by lack of decision support tools that can in-corporate security into the decision making process. Thecurrent practice is to protect the system against knownor anticipated failures either by using a post-processingphase or by explicit enumeration of the know cases. Theseapproaches not only lack scalability to larger systems orhigher security standards, but also are limited to predictedfailures, which is a significant shortcoming with the uncer-tainty of the renewable generation. In our earlier work, wehave developed efficient techniques for vulnerability analy-sis of electric power systems. We are now in the process ofadding our vulnerability analysis techniques into the deci-sion making process. Specifically, we are investigating analternative formulation of security-constrained unit com-mitment problem. The key to our approach is our abilityto compactly represent security constraints. In this talk,we will present our security formulations, and our resultsfor solving the security-constrained unit-commitment prob-lem.

Ali PinarSandia National [email protected]

Jean-Paul WatsonSandia National LaboratoriesDiscrete Math and Complex [email protected]

MS68

L1 Fitting for Nonlinear Parameter IdentificationProblems for PDEs

For parameter identification problems where the measureddata is corrupted by impulsive noise, L1-data fitting ismore robust than conventional L2-fitting. However, thisleads to a non-smooth optimization problem. In this talk,an approach for the numerical solution of parameter identi-fication for PDEs with L1-data fitting is presented and an-alyzed. This approach is based on a semi-smooth Newtonmethod and shows locally superlinear convergence. Theeffectiveness is illustrated through numerical examples.

Christian ClasonUniversity of GrazInstitute for Mathematics and Scientific [email protected]

MS68

Simultaneous Identification of Multiple Coeffi-cients in an Elliptic PDE

We consider the inverse problem of determining multi-ple, piecewise analytic coefficients in an elliptic PDE fromboundary measurements. Based on the theory of localizedpotentials, we are able to give an exact theoretical char-acterization of the reconstructible information. We alsodiscuss the consequences of this injectivity result to prac-

tical reconstruction schemes.

Bastian HarrachDepartment of Mathematics - M1Technische Universitat [email protected]

MS68

Nonsmooth Regularization and Sparsity Optimiza-tion

The sparsity optimization for the linear least square prob-lem is considered. The problem is formulated as non-smooth regularization problem. The necessary optimalitycondition is derived and a numerical algorithm to deter-mine a solution is developed and analyzed. The propertyof solutions and the optimal value function as a functionof the regularization parameter is analyzed. Various se-lection principle and algorithms for determining the reg-ularization parameter are developed and analyzed for thesparisity regularization based on the analysis of the optimalvalue function.

Kazufumi ItoNorth Carolina State UniversityDepartment of [email protected]

MS68

Error Estimates for joint Tikhonov and LavrentievRegularization of Parameter Identification Pro-belms

Problems of optimal control often involve constraints bothon the control and on the state of the system, but the so-lution may not be stable to calculate. Hence, one oftenemploys Tikhonov regularization. Then the resulting opti-mization problem may still be difficult to solve due to lowregularity of Lagrange multipliers. This difficulty can beovercome by Lavrentiev-type regularization. In this talk.error estimates for this kind of doubly regularized problemsare derived.

Dirk LorenzTechnical University of [email protected]

Arnd RoschUniversity of [email protected]

MS69

On Some Strategies for Jacobian-free Precondition-ing of Sequences of Nonsymmetric Linear Systems

An appealing property of Newton-Krylov methods forthe solution of nonlinear algebraic systems is that theylend themselves well for matrix-free implementations wheremultiplication with the Jacobian is replaced by a differenceapproximation. However, this makes the computation ofrobust LU-type preconditioners for the Jacobians signifi-cantly more challenging. In this talk we address variousmatrix-free preconditioning techniques for the special casewhere we wish to update preconditioners from previous lin-ear systems.

Jurjen Duintjer TebbensInstitute of Computer SciencesAcademy of Sciences of the Czech Republic, Prague

OP11 Abstracts 147

[email protected]

Miroslav TumaAcademy of Sciences of the Czech RepublicInstitute of Computer [email protected]

MS69

Limited-memory Preconditioners for Large SparseLeast-squares Problems

We present a technique for constructing incomplete LDLT

preconditioners for the normal equation matrix of largeand sparse linear least-squares problems. The precondi-tioners obtained can be interpreted as approximate sparseinverse preconditioners. The construction of the precondi-tioners is breakdown-free and does not need to form thenormal matrix. Only matrix-vector products are requiredand transpose-free implementations are possible. The den-sity and sparsity pattern is fixed in advanced and limitedintermediate storage is needed. Numerical experiments areshown.

Benedetta MoriniUniversita’ di [email protected]

Stefania BellaviaUniversita di [email protected]


MS69

Multipreconditioned GMRES with Applications inPDE-constrained Optimization

The bottleneck in many algorithms for solving large scaleoptimization problems is the solution of a saddle point sys-tem. A common way to do this is by using a Krylov sub-space method, which needs to be coupled with a suitablepreconditioner to be effective. For a saddle point problemsthere are a number of possible choices of preconditioner– e.g. constraint or block diagonal preconditioners – andin certain cases one or another may be a better choice. Inthis talk we present multipreconditioned GMRES (MPGM-RES), which is an algorithm that extends GMRES by auto-matically combining the properties of more than one pre-conditioner in an optimal way. We will demonstrate theeffectiveness of the algorithm by applying it to systemsfrom problems in PDE-constrained optimization.

Tyrone ReesDepartment of Computer Science,University of British Columbia, [email protected]

Chen GreifDepartment of Computer ScienceThe University of British [email protected]

MS69

Parallel Algebraic Multilevel Preconditioners for

PDE-Constrained Optimization

We investigate the application of parallel multileveldomain-decomposition preconditioners to linear systemsarising from the discretization of optimality systems forelliptic optimal control problems. We focus on algebraicmultilevel Schwarz preconditioners with smoothed aggre-gation coarsening, that are modified to take into accountthe block structure that results from a suitable ordering ofthe unknowns. We report results of numerical experimentsperformed on linux clusters with the MLD2P4 package, ex-tended to include the above modifications.

Alfio Borzi’University of SannioDepartment of [email protected]

Valentina De Simone, Daniela di SerafinoSecond University of NaplesDepartment of [email protected],[email protected]

MS70

Ambiguous Probabilistic Set Covering

We consider probabilistic set covering constraints, wherethe covering coefficients are Bernoulli random variableswith partial distribution information. Using union bounds,we formulate the corresponding ambiguous probabilistic setcovering problem into a deterministic mixed-integer linearprogram. Some strong valid inequalities for the problemare also developed.

Shabbir AhmedH. Milton Stewart School of Industrial & SystemsEngineeringGeorgia Institute of [email protected]

Dimitri PapageorgiouISyEGeorgia [email protected]

MS70

On the Complexity of Non-Overlapping Multivari-ate Marginal Bounds for Probabilistic Combinato-rial Optimization Problems

Given a probabilistic combinatorial optimization problem,we evaluate the tightest bound on the expected opti-mal value over joint distributions with given multivariatemarginals. This bound was first proposed in the PERTcontext by Meilijson and Nadas (Journal of Applied Prob-ability, 1979). New instances of polynomial time com-putable bounds are identified. An important feature ofthe bound we propose is that it is exactly achievable by ajoint distribution, unlike many of the existing bounds.

Karthik NatarajanDepartment of Management SciencesCity University of Hong [email protected]

Xuan Vinh DoanDepartment of Combinatorics and OptimizationUniversity of Waterloo

148 OP11 Abstracts

[email protected]

MS70

Multiple Objectives Satisficing under Uncertainty

We propose a class of functions, called multiple objectivesatisficing (MOS) criteria, for evaluating the level of com-pliance of the objectives in meeting their targets collec-tively under uncertainty. The MOS criteria include thejoint targets’ achievement probability (success probabilitycriterion) as a special case and also extend to situationswhen the probability distribution is not fully character-ized or ambiguity. We focus on a class of MOS criteriathat favors diversification, which has the potential to mit-igate severe shortfalls in scenarios when an objective failsto achieve its target. Naturally, this class excludes suc-cess probability and we propose the shortfall-aware MOScriterion (S-MOS), which is diversification favoring and isa lower bound to success probability. We show how tobuild tractable approximations of S-MOS that preservesthe salient properties of MOS. We report encouraging com-putational results on a refinery blending problem in meet-ing specification targets even in the absence of full distri-butional information.


MS70

On Safe Tractable Approximations of Chance Con-strained Linear Matrix Inequalities with Partly De-pendent Perturbations

In this talk, we will demonstrate how tools from probabil-ity theory can be used to develop safe tractable approx-imations of chance constrained linear matrix inequalitieswith partly dependent data perturbations. An advantageof our approach is that the resulting safe tractable approx-imations can be formulated as SDPs or even SOCPs, thusallowing them to be solved easily by off-the-shelf solvers.We will also discuss some applications of our results.

Anthony SoThe Chinese University of Hong [email protected]

MS71

Derivitive Approximation in Optimization for Sta-tistical Learning

Optimization problems that occur in machine learning aredifficult mainly because of the expense of computing gradi-ent and function values for large data sets. We discuss useof algorithms based on standard concepts such as truncatedNewton, that use small-sample approximations to gradi-ents and Hessians. We compare them to some of the specialpurpose machine learning algorithms that have been de-veloped. We present computational experiments on someexamples and also give some complexity results.

Richard H. ByrdUniversity of [email protected]

MS71

Preconditioning and Globalizing Conjugate Gra-dients in Dual Space for Quadratically Penalized

Nonlinear-Least Squares Problems

We consider the Gauss-Newton algorithm for solving non-linear least-squares problems, regularized with a quadraticterm, that occur in data assimilation with application toMeteorology or Oceanography. Each quadratic problem ofthe method is solved with a dual space conjugate-gradient-like method. The use of an effective preconditioning tech-nique is proposed and refined convergence bounds derived,which results in a practical solution method. Finally, stop-ping rules adequate for a trust-region solver are proposedin the dual space.

Serge GrattonCERFACSToulouse, [email protected]

MS71

Infeasibility Detection in Nonlinear Programming

We describe an interior point algorithm with infeasibilitydetection capabilities. By employing a feasibility restora-tion phase, the new algorithm can give promote fast conver-gence to infeasible stationary points, or when the problemis feasible, fast convergence to a KKT point. We also de-scribe analysis that shows how two-step active set methodsthat base the step computation on an appropriate model ofthe penalty function, can give fast infeasibility detection.

Figen OztoprakSabanci [email protected]

MS71

Updating Rules for the Regularization Parameterin the Adaptive Cubic Overestimation Method

The Adaptive Cubic Overestimation method has been re-cently proposed for solving unconstrained minimizationproblems. At each iteration, the objective function is re-placed by a cubic approximation which comprises an adap-tive regularization parameter that estimates the Lipschitzconstant of the objective. We present new updating strate-gies for this parameter based on interpolation techniqueswhich improve the overall numerical performance of the al-gorithm. Numerical experiments on large nonlinear least-squares problems are shown.


Margherita PorcelliDepartment of Mathematics and naXysFUNDP - University of [email protected]


MS72

Semidefinite Relaxations for Non-Convex

OP11 Abstracts 149

Quadratic Mixed-Integer Programming

We present semidefinite relaxations for unconstrained non-convex quadratic mixed-integer optimization problems.These relaxations yield tight bounds and are computa-tionally easy to solve for medium-sized instances, even ifsome of the variables are integer and unbounded. In thiscase, the problem contains an infinite number of linear con-straints; these constraints are separated dynamically. Weuse this approach as the bounding routine in an SDP-basedbranch-and-bound framework. In case of a convex objec-tive function, the new SDP bound improves the boundgiven by the continuous relaxation of the problem. Numer-ical experiments show that our algorithm performs well onvarious types of non-convex instances.

Christoph BuchheimTU [email protected]

Angelika WiegeleAlpen-Adria-Universit{”a}t KlagenfurtInstitut f. [email protected]

MS72

Safe Coloring of Large Graphs

One of the best methods for determining the chromaticnumber of a graph is the linear-programming branch andprice technique. We present an implementation of themethod that provides numerically safe results, independentof the floating-point accuracy of the LP solver. We pro-pose an improved branch-and-bound algorithm for findingmaximum-weight stable sets that enables us closing previ-ously open DIMACS benchmarks. Finally, computationalresults on standard benchmarks as well as an applicationfrom VLSI-design are presented.

Stephan HeldUniversity of [email protected]

Edward SewellSouthern Illinois University [email protected]


MS72

Dantzig-Wolfe Reformulations of General MixedInteger Programs

We discuss how Dantzig-Wolfe reformulations can be ap-plied to general Mixed Integer Programs (MIP), which donot necessarily have an explicit or implicit block-diagonalstructure, so as to obtain stronger formulations. We showthat by looking for almost block-diagonal structures, ap-plication of Dantzig-Wolfe reformulation leads to improvedresults with respect to the direct application of a generalMIP solver to the original formulation. We briefly discussfeatures which characterize an effective reformulation.

Martin BergnerRWTH, Aachen [email protected]

Alberto Caprara, Fabio FuriniDEIS - University of [email protected], [email protected]

Marco LuebbeckeRWTH, Aachen [email protected]

Enrico MalagutiDEIS - University of [email protected]

Emiliano TraversiUniversity of [email protected]

MS72

Computational Evaluation of Verification Cuts

An inequality cT x ≤ d with integral coefficients for an inte-ger program yields a verification cut if cT x ≥ d+1 containsno solution to the integer program. Verification cuts can beshown to yield strong cuts in many cases. We investigatethe computational use of these cuts. Different methods toproduce a base inequality cT x ≤ d and different ways toprove infeasibility of the complementary cut via truncatedbranch-and-cut are considered.

Marc E. PfetschTU [email protected]

Santanu DeyGeorgia [email protected]


MS73

Regularization and Shifted Barriers for Linear Pro-gramming

We consider the classical problem of solving a linear pro-gram. Our concern is regularization of the problem byshifted barriers and quadratic penalties. We discuss theuse of regularizations based on different norms. In addi-tion, we discuss how to solve the problem by a primal-dualapproach based on simplex-like steps or an interior method.

Anders Forsgren

Royal Institute of Technology (KTH)Dept. of [email protected]

MS73

Incremental Newton-type Methods for Data Fit-ting

In many structured data-fitting applications, frequent dataaccess is the main computational cost. Incremental-gradient algorithms (both deterministic and randomized)offer inexpensive iterations by sampling only subsets of thedata. These methods can make great progress initially,but often stall as they approach a solution. In contrast,

150 OP11 Abstracts

Newton-type methods achieve steady convergence at theexpense of frequent data access. We explore hybrid meth-ods that exhibit the benefits of both approaches. Numer-ical experiments illustrate the potential for the approach.

Michael P. FriedlanderDept of Computer ScienceUniversity of British [email protected]

MS73

A Gauss-Newton-Type Method for ConstrainedOptimization Using Differentiable Exact Penalties

We propose a Gauss-Newton-type method for nonlinearconstrained minimization problems, using an extension ofthe exact penalty for variational inequalities, introducedrecently by Andre and Silva. The exact penalty is con-structed based on the incorporation of a multiplier estimatein an augmented Lagrangian. Using a weaker assumption,we prove exactness and convergence results. A globaliza-tion idea is also established, as well as some numerical ex-periments with the CUTE collection.

Ellen H. FukudaUniversity of So [email protected]

Paulo J. S. SilvaUniversity of Sao [email protected]

Roberto [email protected]

MS73

Iterative Methods for SQD Linear Systems

Symmetric quasi-definite (SQD) systems arise naturallyin interior-point methods for convex optimization and insome regularized PDE problems. In this talk we reviewthe connection between SQD linear systems and other re-lated problems and investigate their iterative solution. Wereport on preliminary numerical experience with an imple-mentation of a regularization method for convex quadraticprogramming.

Dominique OrbanGERAD and Dept. Mathematics and IndustrialEngineeringEcole Polytechnique de [email protected]

Mario ArioliRutherford Appleton LaboratoryChilton, [email protected]

MS74

System-theoretic Methods for Model Reduction ofLinear and Nonlinear Parabolic Systems

We discuss model reduction methods based on ideas fromsystem theory. These methods rely on considering (gen-eralized) transfer functions of the describing state and ob-servation equations. For parabolic systems, these could be

formulated in the infinite-dimensional setting or after spa-tial discretization of the state variables. We will focus onthe latter approach, and review methods based on balancedtruncation as well as Krylov subspace methods for linearand nonlinear problems.

Peter BennerMax-Planck-Institute forDynamics of Complex Technical [email protected]

Tobias BreitenMax-Planck-Institute for Dynamics of Complex TechnicalSystems, [email protected]

MS74

Model Reduction Methods in the Calibration ofFinancial Market Models

The calibration of models for derivative pricing is an im-portant application of optimization in finance. The useof reduced order models improves the efficiency of the nu-merical scheme substantially. We review various venues forthe use of reduced order models and discuss in particularproper orthogonal decomposition with a trust region vari-ant. We illustrate the claims with numerical results for thecalibration of a PIDE.


MS74

Applications of DEIM in Nonlinear Model Reduc-tion

A dimension reduction method called Discrete EmpiricalInterpolation (DEIM) is described and shown to dramati-cally reduce the computational complexity of the popularProper Orthogonal Decomposition (POD) method for con-structing reduced-order models for parametrized nonlinearpartial differential equations (PDEs). DEIM is a techniquefor reducing the complexity of evaluating the reduced ordernonlinear terms obtained with the standard POD-Galerkin.POD reduces dimension in the sense that far fewer vari-ables are present, but the complexity of evaluating the non-linear term remains that of the original problem. DEIM isa modification of POD that reduces complexity of the non-linear term of the reduced model to a cost proportional tothe number of reduced variables obtained by POD. Themethod applies to arbitrary systems of nonlinear ODEs,not just those arising from discretization of PDEs. In thistalk, the DEIM method will be developed along with adiscussion of its approximation properties. Applicationsin Shape Optimization and PDE constrained optimizationshall be emphasized. Additional applications from Chemi-cally Reacting Flow and Neural Modeling will be presentedto illustrate the effectiveness and wide applicability of theDEIM approach.

Danny C. Sorensen, Saifon ChaturantabutRice [email protected], [email protected]

MS74

Error Control in POD and RB Discretizations of

OP11 Abstracts 151

Nonlinear Optimal Control Problems

In the talk a-posteriori error estimation is utilized to con-trol Galerkin-based reduced-order models for optimal con-trol problems governed by nonlinear partial differentialequations. More precisely, the nonlinear problems aretreated by an inexact second-order methods, where the in-exactness is handled using a-posteriori error analysis. Thepresented numerical strategies are illustrated for the PODand the Reduced-Basis method.

Stefan VolkweinUniversitat [email protected]

MS75

Computational Methods for Equilibrium: Makingthe Most of Optimization

Many phenomena are modeled as equilibrium problemsconsisting of simultaneous optimization by multiple agents(MOPEC). In the case of Walrasian equilibrium, we con-sider solution methods that solve a sequence of optimiza-tion subproblems for only one agent at a time. We showhow to guide this sequence so that the algorithm converges.

Jesse HolzerUniversity of Wisconsin - MadisonMadison, [email protected]

MS75

Regularization Methods for Mathematical Pro-grams with Complementarity Constraints

Mathematical programs with complementarity constraintsform a difficult class of optimization problems. Standardconstraint qualifications are typically violated. Therefore,more specialized algorithms are applied. A popular methodis the regularization scheme by Scholtes. In the meantime,however, there exist a number of different regularizationapproaches for the solution of MPCCs. Here we first givea survey of the existing methods, introduce a new one,and improve the existing convergence assumptions of mostmethods.

Christian KanzowUniversity of [email protected]

Tim HoheiselUniversity of Wurzburg97074 Wurzburg, [email protected]

Alexandra SchwartzUniversity of WurzburgInstitute of [email protected]

MS75

Effort Maximization in Asymmetric ContestGames with Heterogeneous Contestants – A BilevelProblem in Economy

We model the lobbying process between a politician andlobbyists as a contest game where the politician can en-courage or discourage specific lobbyists from participating.

This extension of the seminal lobbying set-up has impor-tant implications: The politician will optimally level theplaying field by encouraging weak lobbyists to participateand at least three lobbyists will be active in the leveledlobbying process. Results are established using the implicitprogramming approach for bilevel problems.

Alexandra SchwartzUniversity of WurzburgInstitute of [email protected]

Jorg FrankeUniversity of Dortmund (TU)Department of [email protected]

Christian KanzowUniversity of [email protected]

Wolfgang LeiningerUniversity of Dortmund (TU)Department of [email protected]

MS75

Convergence Analysis for Path-Following MethodsApplied to Optimal Control Problems Subject toAn Elliptic Variational Inequality

In the talk, we consider the approximate solution of an op-timal control problem subject to an elliptic variational in-equality. The resulting optimization problem is an infinite-dimensional MPCC. The problem is regularized in the fol-lowing way: The variational inequality is replaced by asemilinear elliptic equation. Existence of solutions of theregularized problem is shown. Moreover, these solutionsdepend continuously and Frechet differentiably on the reg-ularization parameter. Convergence of the regularized so-lutions to a solution of the original MPCC is proven to-gether with convergence rates with respect to the regular-ization parameter.

Daniel WachsmuthJohann Radon Institute for Computational and AppliedMathematics, Linz, [email protected]

Karl KunischKarl-Franzens University GrazInstitute of Mathematics and Scientific [email protected]

Anton SchielaZIB, [email protected]

MS76

Extended Formulations in Mixed-Integer Program-ming

Several problems in the optimal planning of productionschedules can be formulated as mixed-integer programs.Extended formulations strengthen the original formulationby adding further variables. We review several techniquesto construct extended formulations. We characterize caseswhere the extended formulation provides the characteri-

152 OP11 Abstracts

zation of the convex hull of the feasible set in a higherdimensional space. We discuss cases where the projectionof the extended formulation can explicitly computed.

Michele ConfortiUniversita degli Studi di [email protected]

MS76

Combinatorial Bounds on Nonnegative Rank andExtended Formulations

In a breakthrough paper, Yannakakis (1991) proved that allsymmetric extended formulations of the perfect matchingpolytope have exponential size. Very little is known aboutgeneral lower bounds the sizes of extended formulations.We investigate a natural general lower bound, namely, theminimum number of combinatorial rectangles needed tocover the support of the slack matrix of the polytope.

Samuel FioriniUniversite Libre de [email protected]

Volker Kaibel, Kanstantsin Pashkovich, Dirk TheisOtto-von-Guericke Universitat [email protected], [email protected],[email protected]

MS76

Symmetry of Extended Formulations for Matching-Polytopes

Yannakakis proved in 1991 that there are no symmet-ric polynomial size extended formulations for the perfectmatching polytopes of complete graphs. He furthermoreconjectured that asymmetry cannot help to obtain polyno-mial size extensions for these polytopes. We prove that,however, the convex hulls of the characteristic vectors ofmatchings of logarithmic size in a complete graph do admitpolynomial size non-symmetric extensions, while all sym-metric extensions of these polytopes have super-polynomialsizes.

Volker Kaibel, Kanstantsin Pashkovich, Dirk TheisOtto-von-Guericke Universitat [email protected], [email protected],[email protected]

MS76

Tight Lower Bound on the Sizes of Symmetric Ex-tensions of Permutahedra

It is well known that the Birkhoff polytope provides a sym-metric extended formulation of the permutahedron Πn ofsize Θ(n2). Recently, Goemans described asymptoticallyminimal extended formulation of Πn of size Θ(n log n).In this paper, we prove that Ω(n2) is a lower bound forthe size of symmetric extended formulations of Πn. Thus,it is possible to determine tight lower bounds Ω(n2) andΩ(n log(n)) on the sizes of symmetric and non-symmetricextended formulations of Πn .

Kanstantsin PashkovichOtto-von-Guericke Universitat [email protected]

MS77

Nonlinear Mpc in the Microsecond Range Us-ing An Auto-Generated Real-Time Iteration Algo-rithm

We present a strategy for automatic C-code generation ofreal-time nonlinear model predictive control (MPC) algo-rithms, which are designed for applications with kilohertzsample rates. The corresponding software module for ex-porting the code has been implemented within the soft-ware package ACADO Toolkit. Its symbolic representationof optimal control problems allows to auto-generate opti-mized plain C-code. The exported code comprises a fixedstep-size integrator that also generates the required sen-sitivity information as well as a real-time Gauss-Newtonmethod that is tailored for final production. Numericalresults show that the exported code has a promising com-putational performance allowing to apply nonlinear MPCto nontrivial processes at sampling times in the milli- andmicrosecond range.

Joachim FerreauK.U. [email protected]

Boris HouskaKU [email protected]


MS77

Solving Linear Complementarity Problems withFast Numerical Methods

In this talk we will show how to improve the speed of firstorder methods for solving linear complementarity problems(LCPs). Specifically, we will concentrate on the numericalsolution of LCPs that arise in CPU intensive applicationssuch as rigid body dynamics and the pricing of Americanoptions. The methodology consists in interlacing first or-der iterations with subspace iterations on the free variablesdetected by the first order phase. The subspace phase con-tributes to the resulting method in two aspects: a) theaccurate identification of the active set; b) the speed ofconvergence. Thus, the new method is able to computevery accurate solutions in less time than the original firstorder method.

Jose Luis MoralesDepartamento de Matematicas.ITAM. [email protected]

MS77

A Distributed Newton Method for Network UtilityMaximization

Most existing work uses dual decomposition and subgradi-ent methods to solve Network Utility Maximization (NUM)problems in a distributed manner, which suffer from slowrate of convergence properties. This work develops analternative distributed Newton-type fast converging algo-rithm for solving network utility maximization problemswith self-concordant utility functions. By using novel ma-trix splitting techniques, both primal and dual updates forthe Newton step can be computed using iterative schemes

OP11 Abstracts 153

in a decentralized manner with limited information ex-change. We show that even when the Newton directionand the stepsize in our method are computed within someerror (due to finite truncation of the iterative schemes),the resulting objective function value still converges super-linearly to an explicitly characterized error neighborhood.Simulation results demonstrate significant convergence rateimprovement of our algorithm relative to the existing sub-gradient methods based on dual decomposition.

Asu Ozdaglar, Ermin [email protected], [email protected]

Ali JadbabaieDepartment of Electrical and Systems EngineeringUniversity of [email protected]

MS77

Mixed-Integer Nonlinear Real-Time Optimization

We present work on nonlinear optimal control problemsin real time, where some control functions may only takevalues from a discrete set. Examples are gear choices intransport, or on/off valves in engineering. Our approach isbased on an Outer Convexification with respect to the inte-ger control functions, the direct multiple shooting method,and real-time iterations as first proposed by Diehl, Bock,and Schloder. We discuss theoretical and numerical as-pects.


Christian KirchesInterdisciplinary Center for Scientific ComputingUniversity of Heidelberg, [email protected]

MS78

On the Lasserre Hierarchy of Semidefinite Pro-gramming Relaxations of Convex Polynomial Op-timization Problems

The Lasserre hierarchy of semidefinite programming ap-proximations to convex polynomial optimization problemsis known to converge finitely under some assumptions.[J.B. Lasserre. Convexity in semialgebraic geometry andpolynomial optimization. SIAM J. Optim. 19, 1995–2014,2009.] We give a new proof of the finite convergence prop-erty, that does not require the assumption that the Hessianof the objective be positive definite on the entire feasibleset, but only at the optimal solution.

Etienne De KlerkTilburg [email protected]

Monique LaurentCWI, Amsterdamand Tilburg [email protected]

MS78

SDP Approximation for the Electronic Structures

of Atoms and Molecules

Determining the ground-state energy (lowest energy) of anelectronic system (of an atom or a molecule) is the coreproblem in quantum chemistry. Solving the SDP approxi-mation of this problem is challenging since it requires par-allel computation and high accuracy due to its excellentapproximation values. We will present the computationalresults for the largest dense (Schur complement matrix)SDP solved so far, and further directions tackle this diffi-cult problem.

Mituhiro FukudaTokyo Institute of TechnologyDepartment of Mathematical and Computing [email protected]



MS78

Moment and SDP Relaxation Methods for SmoothApproximations of Nonlinear Differential Equa-tions

Combining moment and semidefinite programming (SDP)relaxation techniques, we propose an approach to findsmooth approximations for solutions of nonlinear differ-ential equations. Given a system of differential equations,we apply a technique based on finite differences and sparseSDP relaxations to obtain a discrete approximation of itssolution. In a second step we apply maximum entropy esti-mation (using moments of a Borel measure associated withthe discrete approximation) to obtain a smooth closed-formapproximation.

Martin [email protected]

Jean Bernard [email protected]

Didier HenrionLAAS-CNRS, University of Toulouse, & Faculty ofElectrical Engineering, Czech Technical [email protected]

MS78

Ellipsoid-type Confidential Bounds on Semi-algebraic Sets via SDP Relaxation

In many applications, we want to know a confidentialbound on semi-algebraic sets. For example, a sensor net-work localization problem is to find a feasible point of semi-algebraic sets. However, if its base network is not rigid, itssensor locations can not be fixed. Our method computes anellipsoid-type confidential bound on semi-algebraic sets viaSDP relaxation. This method can specify the possible re-gion of each sensor even when the network is not rigid. Wealso apply our method to polynomial optimization prob-

154 OP11 Abstracts

lems which have multiple optimal solutions and obtain abound to cover all the optimal solutions.


Masakazu KojimaTokyo Institute of [email protected]

MS80

SDPA Project: Solving Large-scale SemidefinitePrograms

Solving extremely large-scale SDPs has a significant im-portance for the current and future applications of SDPs.In 1995, we have started the SDPA Project aimed for solv-ing large-scale SDPs with numerical stability and accuracy.SDPA and SDPARA are pioneers’ code to solve generalSDPs. In particular, it has been successfully applied onquantum chemistry, the SDPARA on a supercomputer hassucceeded to solve the largest SDP and made a new worldrecord.




Mituhiro FukudaTokyo Institute of TechnologyDepartment of Mathematical and Computing [email protected]

MS80

Which Mixed Integer Programs could a MillionCPUs Solve?

There is a trend in supercomputing to employ evermorecomputing cores. Today, the current top 10 machineshave on average 150000 cores and likely a million coreswill be available soon. The question arises how to harnessthese vast computing capabilities to solve new classes ofmixed integer programs. Based on our experiences withdistributed parallel solvers we will systematically investi-gate under which conditions such a machine might effi-ciently solve MIPs.


Yuji ShinanoZuse Institute BerlinTakustr. 7 14195 [email protected]

MS80

DIP with CHiPPS: Parallelizing Algorithms forSolving Integer Programs

Most practical algorithms for solving integer programs fol-low the basic paradigm of tree search. Such algorithmsare easy to parallelize in principle, but there are manychallenges to achieving scalability in practice. We discussapproaches to overcoming these challenges both using thecourse-grained parallelism afforded by parallelizing the treesearch itself and the fine-grained parallelism afforded byparallelizing the computations that take place in process-ing a single search tree node.

Ted RalphsDepartment of Industrial and Systems EngineeringLehigh [email protected]

Matthew Galati, Yan XuSAS [email protected], [email protected]

MS80

Solving Hard MIP Instances using Massively Par-allelized MIP Solvers

We present parallel implementations of state-of-the-artMIP solvers, CPLEX and SCIP, on a distributed mem-ory computing environment. The implementations are con-structed using a single software framework that enables usto execute sequential branch-and-bound codes in parallel.We show computational results conducted with the paral-lel MIP solvers using up to 7,168 cores of HLRN II. Theseresults include the solutions to two open instances fromMIPLIB2003 that had not been solved yet.

Yuji ShinanoZuse Institute BerlinTakustr. 7 14195 [email protected]

Tobias AchterbergIBM Deutschland Research & Development [email protected]

Timo Berthold, Stefan HeinzZuse Institute BerlinTakustr. 7 14195 [email protected], [email protected]


MS81

A POD Approach to Robust Controls in PDE Op-timization

A strategy for the fast computation of robust controls ofPDE models with random-field coefficients is presented. Arobust control is defined as the control function that min-imizes the expectation value of the objective over all co-efficient configurations. A straightforward application ofthe adjoint method on this problem results in a very largeoptimality system. In contrast, a fast method is presentedwhere the expectation value of the objective is minimizedwith respect to a reduced POD basis of the space of con-

OP11 Abstracts 155

trols. Comparison of the POD scheme with the full opti-mization procedure in the case of elliptic control problemswith random reaction terms and with random diffusivitydemonstrates the superior computational performance ofthe POD-based method.

Alfio BorziInstitute for MathematicsUniversity of [email protected]

Gregory von WinckelUniversity of GrazInstitute of [email protected]

MS81

Stochastic Collocation for Optimization ProblemsGoverned by Stochastic Partial Differential Equa-tions

Many optimization optimization problems in engineeringand science are governed by partial differential equations(PDEs) with uncertainties in the input data. Since the so-lution of such PDEs is a random field and enters the objec-tive function, the objective function usually involves statis-tical moments. Optimization problems governed by PDEswith uncertainties in the input data are posed as a par-ticular class of optimization problems in Bochner spaces.This allows us to use the frameworks for derivative basedoptimization methods in Banach spaces. However numer-ical solution of these problems is more challenging thandeterministic PDE constrained optimization problems, be-cause it requires discretization of the PDE in space/timeas well as in the random variables. We discuss stochas-tic collocation methods for the numerical solution of suchoptimization problems, explore the decoupling nature ofthis method for gradient and Hessian computations as wellas preconditioning, and we present estimates for the dis-cretization error.

Matthias HeinkenschlossRice UniversityDept of Comp and Applied [email protected]

Drew KouriDepartment of Computational and Applied MathematicsRice [email protected]

MS81

Numerical Treatment of Uncertainties in Aerody-namic Shape Optimization

In this talk, a novel approach towards stochastic dis-tributed aleatory uncertainties for the specific applicationof optimal aerodynamic design under uncertainties will bepresented. Proper robust formulations of the determin-istic problem as well as efficient adaptive discretizationtechniques combined with algorithmic approaches based onone-shot methods attacking the additional computationalcomplexity will be discussed. Further, numerical results ofrobust aerodynamic shape optimization under uncertainflight conditions as well as geometrical uncertainties willbe presented.

Claudia SchillingsUniversity of Trier, Germany

[email protected]

Volker SchulzUniversity of TrierDepartment of [email protected]

MS81

Shape Optimization under Uncertainty fromStochastic Programming Point of View

Shape optimization with linearized elasticity understochastic loading bears conceptual similarity with finite-dimensional two-stage linear stochastic programming.Shapes correspond to nonanticipative first-stage decisionsin the stochastic program. The weak formulation of theelasticity pde forms an analogue to the second-stage opti-mization problem. Based on these observations, we presentrisk-neutral and risk-averse stochastic shape optimizationproblems, discuss algorithms for their solution, and reportcomputational results.

Ruediger SchultzUniversity of [email protected]

MS82

Optimization with Risk Via Stochastic DominanceConstraints

The theory of stochastic dominance provides tools to com-pare the distributions of two random variables. Notionsof stochastic dominance have been used in a wide rangeof areas, from epidemiology to economics, as they allowfor comparison of risks. Such concepts are also useful inan optimization setting, where they can be used as con-straints to control for risk – an area that has gained atten-tion in the literature since its introduction by Dentchevaand Ruszczynski in a 2003 paper. The use of stochas-tic dominance in a multivariate setting can then allow formulti-criterion risk comparisons, which is useful not onlyfor optimization but also from a pure decision-making per-spective. The multivariate setting, however, poses signif-icant challenges, as even testing for such conditions maybe difficult. In this talk we introduce some alternativeconcepts based on the notion of multivariate linear dom-inance, where linear combinations of the underlying ran-dom vectors are compared using coefficients from a certainuser-specified set that may represent the opinions of mul-tiple decision makers. When the random vectors beingcompared have discrete distributions, these new stochas-tic dominance relationships can be represented by a finitenumber of inequalities. Moreover, some of these conceptscan be parameterized in order to allow for a relaxation ofthe dominance condition. These results yield concrete con-ditions can be checked, either as stand-alone comparisonsor as constraints in the optimization setting. We discussthese formulations in detail and present some practical ex-amples to illustrate the ideas.

Tito Homem-de-MelloNorthwestern [email protected]

Sanjay MehrotraIEMSNorthwestern [email protected]

156 OP11 Abstracts

Jian HuNorthwestern [email protected]

MS82

Scenario Generation in Stochastic Optimization

Some approaches for generating scenarios in stochastic op-timization are shortly reviewed. The Quasi-Monte Carlo(QMC) approach is discussed in more detail. In partic-ular, we provide conditions implying that QMC may besuccessfully applied to two-stage dynamic stochastic pro-grams and is superior to Monte Carlo. Some numericalexperience is also presented.

Werner RoemischHumboldt-University BerlinInstititute of [email protected]

MS82

Distributed Schemes for Computing Equilibria ofMonotone Nash Games

In this talk, we consider the distributed computation ofequilibria arising in monotone Nash games over continu-ous strategy sets. Direct application of projection-basedschemes are characterized by a key shortcoming: they canaccommodate strongly monotone mappings only. We de-velop single-timescale regularized variants (via Tikhonovand proximal-point methods) that can accommodate amore general class of problems and provide convergencetheory. Several extensions of this framework are stud-ied, including inexact projection schemes, partially coordi-nated generalizations (where players choose steplength se-quences independently) and generalizations to the stochas-tic regime.

Uday ShanbhagDepartment of Industrial and Enterprise SystemsEngineeringUniversity of Illinois at [email protected]

MS82

Stochastic Mathematical Programs with Equilib-rium Constraints

In this talk, we discuss numerical approximation schemesfor a two stage stochastic programming problem wherethe second stage problem has a general nonlinear com-plementarity constraint: first, the complementarity con-straint is approximated by a parameterized system of in-equalities with a well-known NLP regularization approachin deterministic mathematical programs with equilibriumconstraints; the distribution of the random variables of theregularized two stage stochastic program is then approxi-mated by a sequence of probability measures. By treatingthe approximation problems as a perturbation of the origi-nal (true) problem, we carry out a detailed stability analy-sis of the approximated problems including continuity andlocal Lipschitz continuity of optimal value functions, andouter semicontinuity and continuity of the set of optimalsolutions and stationary points. A particular focus is givento the case when the probability distribution is approxi-mated by the empirical probability measure which is alsoknown as sample average approximation.

Huifu Xu

Southampton [email protected]

MS83

Convex Relaxation for the Clique and ClusteringProblems

Given data with known pairwise similarities, partitioningthe data into disjoint clusters is equivalent to partition-ing a particular graph into disjoint cliques. We considerthe related problem of identifying the maximum subgraphcomprised of k disjoint cliques of a given graph. We showthat this NP-hard problem can be solved exactly by re-laxing to a convex optimization problem by replacing rankwith the nuclear norm for certain input graphs.

Brendan AmesUniversity of [email protected]


MS83

Convex Graph Invariants

The structural properties of graphs are characterized interms of invariants, which are functions of graphs that donot depend on node labeling. We discuss convex graph in-variants, which are graph invariants that are convex func-tions of the adjacency matrix of a graph. Some examplesinclude the maximum degree, the MAXCUT value (andits semidefinite relaxation), and spectral invariants suchas the sum of the k largest eigenvalues. Such functionscan be used to construct convex sets that impose variousstructural constraints on graphs, and thus provide a unifiedframework for solving several interesting graph problemsvia convex optimization.

Venkat Chandrasekaran, Pablo A. Parrilo, Alan WillskyMassachusetts Institute of [email protected], [email protected], [email protected]

MS83

Nuclear Norm of Multilinear Forms and TensorRank

We will define Schatten and Ky Fan norms for tensors ofarbitrary order and discuss their basic properties. In par-ticular, we show that the Schatten 1 norm is the convexenvelope of tensor rank on the spectral norm unit ball –a generalization of a well-known result in matrix comple-tion. We will then discuss how one may compute Schattennorms of a tensor via semidefinite relaxation of a general-ized moment problem.

Lek-Heng LimUniversity of [email protected]

MS83

The Convex Geometry of Linear Inverse Problems

Building on the success of generalizing compressed sensingto matrix completion, we extend the catalog of structuresthat can be recovered from partial information. We de-

OP11 Abstracts 157

scribe algorithms to decompose signals into sums of atomicsignals from a simple, not necessarily discrete, set. Thesealgorithms are derived in a convex optimization frameworkthat generalizes previous methods based on l1-norm andnuclear norm minimization. We discuss general recoveryguarantees for our approach and several example applica-tions.

Benjamin RechtUniversity of Wisconsin – [email protected]

Venkat Chandrasekaran, Pablo A. Parrilo, Alan WillskyMassachusetts Institute of [email protected], [email protected], [email protected]

MS85

Sparse Interpolatory Surrogate Models for Poten-tial Energy Surfaces

In this presentation we describe recent results on manag-ing interpolatory surrogate models for potential energy sur-faces. The objectives are to avoid the use of an expensivesimulator with an interpolatory approximation, keep thenumber of interpolatory nodes at a moderate level for prob-lems of dimension up to ten, and perform well on clusterarchitectures. We will discuss the motivating application,the algorithmic issues, and our solutions. We will also re-port computational results

Carl T. KelleyNorth Carolina State UnivDepartment of Mathematicstim [email protected]

David MokrauerDept of MathematicsNC State [email protected]

MS85

A Linearly-Constrained Augmented LagrangianMethod for PDE-Constrained Optimization

In this talk, I describe a linearly-constrained augmentedLagrangian method for solving PDE-constrained optimiza-tion problems. This method computes two directions, aNewton direction to reduce the constraint violation anda reduced-space direction to improve the augmented La-grangian merit function. The reduced-space direction iscomputed from a limited-memory quasi-Newton approxi-mation to the reduced Hessian. This method requires aminimal amount of information from the user, yet obtainsgood performance on our test problems.

Todd MunsonArgonne National LaboratoryMathematics and Computer Science [email protected]

MS85

Multigrid Methods for PDE-constrained Optimiza-tion

MG/Opt is a multigrid optimization approach for the solu-tion of constrained optimization problems. The approachassumes that one has a hierarchy of models, ordered fromfine to coarse, of an underlying optimization problem, and

that one is interested in finding solutions at the finest levelof detail. MG/Opt uses calculations on coarser levels to ac-celerate the progress of the optimization on the finest level.I discuss convergence results for MG/Opt, along with is-sues affecting performance.

Stephen G. NashGeorge Mason UniversitySystems Engineering & Operations Research [email protected]

MS85

Multilevel Optimization with Reduced Order Mod-els for PDE-Constrained Problems

We present an adaptive multilevel generalized SQP-methodfor optimal control problems governed by nonlinear PDEswith control constraints. During the optimization itera-tion the algorithm generates a hierarchy of adaptively re-fined discretizations. The discretized problems are theneach approximated by an adaptively generated sequenceof reduced order models. The adaptive refinement strate-gies are based on error estimators for the original and thediscretized PDE, adjoint PDE and a criticality measure.Numerical results are presented.

J. Carsten ZiemsTechnische Universitaet [email protected]


MS86

Global Optimization Methods for the Identificationof Biochemical Networks

Model building is a key task in systems biology. In this con-text, model identification often becomes a bottleneck dueto limited amount and low quality of experimental data.The discrimination among different model candidates facessimilar challenges. This work revisits the problems of pa-rameter estimation and the optimal experimental designas challenging non-linear (dynamic) optimization problemsand shows, through some examples, how to handle thiscomplexity by means of suitable global optimization tech-niques.

Eva [email protected]

Julio R. BangaIIM-CSICVigo, [email protected]

MS86

Reverse Engineering of Gene Expression via Opti-mal Control

Many cellular networks have evolved to maximize fit-ness. Experimental and numerical observations suggestthat gene onset in bacterial amino acid metabolism followsa “just-in-time’ pattern that can be understood as the so-lution of a dynamic optimization problem. Here we use

158 OP11 Abstracts

rigorous tools such as the Minimum principle and Linear-Quadratic optimization to reverse engineer genetic timing.Our analysis suggests new hypotheses about the generalvalidity of this design principle.

Diego A. OyarzunDepartment of BioengineeringImperial College [email protected]

MS86

Optimal Design of Transcription Networks

The ongoing advance in synthetic biology allows for theimplementation of artificial biochemical networks with in-creasing complexity and accuracy. This calls for the useof computational methods to cope with the design processand avoid inefficient try and error approaches. Every sys-tem is subject to random perturbations and uncertaintiesand trying to optimize the worst case performance leadsto nonlinear semi-infinite min-max optimization problemswhich we solve by replacing them with a sequence of fi-nite dimensional non linear programs. The method is il-lustrated by optimizing and stabilizing the period of thecircadian oscillator of Drosophila.

Marcel RehbergFreiburg University, [email protected]

Dominik SkandaDepartment of Applied MathematicsUniversity of Freiburg, [email protected]

Dirk LebiedzUniversity of FreiburgCenter for Systems [email protected]

MS86

Robustness Analysis of Biomolecular Networks viaPolynomial Programming

Dynamical models of biomolecular networks commonlycontain significant parametric uncertainty, which affectsthe model behaviour and the network’s related biologicalfunction. The talk presents methods of polynomial pro-gramming which allow to quantify the effects of uncertain-ties on the model behaviour, and to compute a level ofparametric uncertainty up to which no significant changesin the qualitative model behaviour occur. In this way, therobustness analysis problem can be handled via a convexoptimization approach.

Steffen WaldherrInstitute for Systems Theory and Automatic ControlUniversitat [email protected]

Frank AllgowerInstitute for Systems Theory in EngineeringUniversity of [email protected]

MS87

Convex Hulls for Non-convex Mixed Integer

Quadratic Programs

We study six families of unbounded convex sets that areassociated with non-convex mixed-integer quadratic pro-grams. The six cases arise by permitting the variables tobe either continuous, integer-constrained, or mixed, and byspecifying them to be either non-negative or free. It turnsout that none of these convex sets are polyhedra. Never-theless, we show that most of them have infinitely manyfacets.

Samuel BurerUniversity of IowaDept of Management [email protected]

Adam N. LetchfordLancaster University Management [email protected]

MS87

Lower Bounds for the Chvtal-Gomory Closure inthe 0/1 Cube

Although well studied, important questions on the rank ofthe Chvtal-Gomory operator when restricting to polytopesin the n-dimensional 0/1 cube have not been answered yet.In this paper we develop a simpler method to establishlower bounds. We show the power and applicability ofthis method on classical examples as well as provide newfamilies of polytopes with high rank. Furthermore, we pro-vide a deterministic family of polytopes achieving a Chvtal-Gomory rank of at least (1+1/e)n - 1 and we show how toobtain a lower bound on the rank from solely examiningthe integrality gap.


Gautier StaufferUniversity of Bordeaux [email protected]

MS87

The Stable Set Polytope of Claw-free Graphs : Ex-tended Formulations, Optimization and Separation

In this talk, we show how recent algorithmic ideas for opti-mizing over the stable polytope of claw-free graphs can bestraightforwardly converted into an extended formulationfor this problem. We then explain how to exploit similarideas to build another extended formulation from the verybasic definition of the convex hull. Finally, building uponthose results, we discuss how to derive a polytime sepa-ration routine and retrieve the linear description in theoriginal space.

Yuri FaenzaUniversita degli Studi di Padovayuri faenza ¡[email protected]¿

Gianpaolo OrioloUniversita di Tor Vergatagianpaolo oriolo ¡[email protected]¿

Gautier StaufferUniversity of Bordeaux [email protected]

OP11 Abstracts 159

MS87

2-clique-bond of Stable Set Polyhedra

A 2-clique-bond is a generalization 2-clique-join where thesubsets of nodes that are connected on each shore of thepartition are two (not necessarily disjoint) cliques. Westudy the polyhedral properties of the stable set polytopeof a graph G obtained as the 2-clique-bond of two graphsG1 and G2. In particular, we prove that a linear descrip-tion of the stable set polytope of G is obtained by properlycomposing the linear inequalities describing the stable setpolytopes of smaller graphs that are related to G1 and G2.

Paolo VenturaIstituto di Analisi dei Sistemi ed [email protected]

MS88

Semidefinite Code Bounds Based on QuadrupleDistances

Error correcting codes are stable sets in highly symmetric,but exponential sized graphs. Exploiting this symmetryallows to transform SDP bounds for the stability num-ber into effective coding bounds. A striking example isthe Lovasz theta bound, which yields a linear sized LP:Delsarte’s bound. We present a stronger bound based onquadruples of code words. The feasible region of our SDPconsists of matrices indexed by pairs of words, that are in-variant under the symmetries of the Hamming cube. Usingrepresentation theory of the symmetric group, the invari-ant algebra can be block diagonalized, allowing the boundto be computed in polynomial time. Computationally, weobtain several improved bounds. In particular we find thatthe quadruply shortened Golay code is optimal.

Dion GijswijtCWI, AmsterdamLeiden [email protected]

MS88

New SDP Relaxations of Stable Set Problems inHamming Graphs

We provide a new upper bound on the maximal size ofthe stable set in Hamming graphs via a new semidefiniteprogramming (SDP) relaxation. Our approach based on anSDP relaxation of the more general quadratic assignmentproblem. We show how to exploit group symmetry in theproblem data and get a much smaller SDP problem in thisspecial case.

Marianna NagyTilburg University, The [email protected]

Etienne De Klerk, Renata SotirovTilburg [email protected], [email protected]

MS88

SDP Versus Eigenvalue Approaches to Bandwidthand Partition Problems

Bandwidth and partition problems are in general NPcomplete. As combinatorial optimization problems theyhave natural formulations in binary variables involving

quadratic constraints. We consider eigenvalue based re-laxations, which are suitable for large scale problems. Theweight redistribution idea allows to tighten these eigen-value bounds. We present some preliminary computationalresults which compare favourably with previous eigenvaluebased relaxations.

Franz RendlUniversitat KlagenfurtInstitut fur [email protected]

Abdel LisserParis [email protected]

Mauro PiacentiniLa Sapienza, [email protected]

MS88

Comparison of Bounds for Some CombinatorialOptimization Problems

In this talk we relate several semidefinite programming re-laxations for the graph partition problem and the band-width problem in graphs, such as those of Donath-Hoffman, Karisch-Rendl, Wolkowicz-Zhao, Zhao-Karisch-Rendl-Wolkowicz. We also present new bounds for thementioned problems that are competitive with previouslyknown ones.

Renata SotirovTilburg [email protected]

MS89

A Two-Scale Approach for Optimization of FineScale Geometry in Elastic Macroscopic Shapes

We investigate macroscopic geometries with geometric de-tails located on a regular lattice. These details are sup-posed to be parametrized via a finite number of parame-ters over which we optimize. Achieved results reveal phe-nomena on different length scales and reflect the multiscalenature of the optimization problem. Hence, we employ atwo-scale approach based on boundary elements for theelastic problem on the microscale and finite elements onthe macroscale. Effective material properties will be stud-ied and relations to laminate based optimization will beinvestigated.

Benedict GeiheRheinische Friedrich-Wilhelms-Universitat BonnInstitut fur Numerische [email protected]

MS89

Shape Optimization with Stochastic DominanceConstraints

Bringing together stochastic and shape optimization, weinvestigate elastic structures under random volume andsurface forces. Drawing on concepts from linear two-stagestochastic programming we formulate shape optimizationmodels with stochastic dominance constraints. The lattersingle out shapes, whose compliances compare favourablywith preselected benchmark random variables. In our algo-

160 OP11 Abstracts

rithms, shape variations arise from parametric shape des-critions, leading to nonlinear programs in finite dimension.Illustrative computational results complete the talk.

Martin PachUniversity of Duisburg-EssenDepartment of [email protected]

MS89

On Certain and Uncertain Aerodynamic Shape Op-timization

Almost any technical process is prone to uncertainties with-ine the model describing this process. Aerodynamic shapeoptimization is one challenging example as part of this gen-eral problem class. We will highlight the challenges causedby uncertainties present in aerodynamics and shape opti-mization and also give ideas for the numerical treatmentof these challenges. Numerical results achieved within col-laborative efforts together with aircraft industry and theGerman Aerospace center will be presented.

Volker SchulzUniversity of TrierDepartment of [email protected]

Stephan SchmidtUniversity of [email protected]

Claudia SchillingsUniversity of Trier, [email protected]

MS90

A Space Mapping Approach for the p-LaplaceEquation

Motivated by car safety applications the goal is to de-termine a thickness coefficient in the nonlinear p-Laplaceequation. The associated structural optimization problemis hard to solve. Therefore, the computationally expensive,nonlinear equation is replaced by a simpler, linear model.A space mapping technique is utilized to link the linear andnonlinear equations and drives the optimization iterationof the nonlinear equation using the fast linear equation.Numerical examples illustrate the presented approach.

Oliver LassUniversitaet [email protected]

Stefan VolkweinUniversitat [email protected]

MS90

Variable-fidelity Design Optimization of Airfoils us-ing Surrogate Modeling and Shape-preserving Re-sponse Prediction

A computationally efficient methodology for airfoil designoptimization is presented. Our approach exploits a cor-rected physics-based low-fidelity surrogate that replaces,in the optimization process, an accurate but computation-ally expensive high-fidelity airfoil model. Correction of

the low-fidelity model is achieved by aligning the airfoilsurface pressure distribution with that of the high-fidelitymodel using a shape-preserving response prediction tech-nique. We present several numerical applications to airfoildesign for both transonic and high-lift conditions.

Slawomir Koziel, Leifur LeifssonReykjavik UniversitySchool of Science and [email protected], [email protected]

MS90

Optimal Control of Particles in Fluids

We present techniques for optimizing particle dispersionsflows and show the application spectrum, power and effi-ciency of space mapping approaches that are based on ahierarchy of models ranging from a complex to a simpleone. Space mapping allows for the easy and efficient treat-ment of stochastic design problems. To control the randomparticle dynamics in a turbulent flow we suggest a Monte-Carlo aggressive space mapping algorithm that yields veryconvincing numerical results.

Rene PinnauTechnische Universitat KaiserslauternFachbereich [email protected]

MS90

Surrogate-Based Optimization for Marine Ecosys-tem Models

Understanding the oceanic CO2 uptake is of central impor-tance for projections of climate change and oceanic ecosys-tems. The underlying models are governed by coupled sys-tems of nonlinear parabolic partial differential equationsfor ocean circulation and transport of biogeochemical trac-ers. The aim is to minimize the misfit between parameterdependent model output and given data. Here we showthat using cheaper surrogate models significantly reducesthe optimization cost.

Malte PrieChristian-Albrechts-Universitaet [email protected]

Thomas SlawigChristian-Albrechts-Uni KielDepartment of Computer [email protected]

Slawomir KozielReykjavik UniversitySchool of Science and [email protected]

PP1

Optimality Conditions and Duality in Nondifferen-tiable Multiobjective Programming

A nondifferentiable multiobjective problem is considered.Fritz John and Kuhn-Tucker type necessary and sufficientconditions are derived for a weak efficient solution. Kuhn-Tucker type necessary conditions are also obtained for aproperly efficient solution. Weak and strong duality theo-rems are established for a Mond-Weir type dual. Moreover,for a converse duality theorem we discuss a special case of

OP11 Abstracts 161

nondifferentiable multiobjective problem, where subgradi-ents can be computed explicitly.

Izhar AhmadKing Fahd University of Petroleum and [email protected]

PP1

Adjoint-Based Full-Waveform Inversion for Param-eter Identification in Seismic Tomography

We present a Newton-type method for full-waveform seis-mic inversion and propose a misfit criterion based onthe convolution and the L2-distance of observed and sim-ulated seismograms. The implementation features theadjoint-based computation of the gradient and Hessian-vector products of the reduced problem, a Krylov subspacemethod to solve the Newton system in matrix-free fashion,spatial discretization of the elastic wave equation by high-order finite elements and parallelization with MPI.

Christian BoehmTechnische Universitaet [email protected]


PP1

An Impulse Control Approach For Dike Height Op-timization

This paper determines the optimal timing as well as theoptimal level of dike updates to protect against floods. Thetrade off is that a dike update (i.e. a dike height increase)is costly, but at the same time such an update reduces theprobability of a flood. In this paper we present the ImpulseControl approach as an alternative method to the DynamicProgramming approach used in Eijgenraam et al. (2010).

Mohammed ChahimDept. of Econometrics & Operations Research, CentERTilburg [email protected]

Ruud Brekelmans, Dick den HertogDept. of Econometrics & Operations Research, CentER,Tilburg [email protected],[email protected]

Peter KortDept. of Econometrics & Operations Research, CentER,TilburgUniversity and Dept. of Economics, University [email protected]

PP1

A New Test-Scenario for Optimization-Based Anal-ysis and Training of Human Decision Making

For computer-based test-scenarios in the domain of com-plex problem solving, the computation of optimal solutionsyields an objective indicator function of participants’ per-formance. However, when these scenarios have been de-

signed, one did not even think of applying mathemati-cal optimization one day, which results in various prob-lems. We present a new model with desirable propertiesfor optimization, which is also capable of extensions tooptimization-based feedback and the inclusion of param-eter estimation, and optimal solutions therefor.

Michael EngelhartHeidelberg UniversityInterdisciplinary Center for Scientific Computing (IWR)[email protected]


Joachim FunkeHeidelberg UniversityDepartment of [email protected]

PP1

Solving Classification Problems by ApproximateMinimal Enclosing Ball Algorithms

Constructing classification models is, under certain hy-potheses, equivalent to the solution of a Minimal Enclos-ing Ball (MEB) problem. Both tasks require the solutionof quadratic programming problems, which in many ap-plications are large and not sparse. We analyze classicalSupport Vector Machine (SVM) methods and new algo-rithms that, exploiting the concept of ε-coreset to com-pute approximate MEBs, can be fruitfully applied in theclassification framework. Experimental results on severalbenchmark datasets are reported.

Emanuele FrandiUniversita degli Studi dell’[email protected]

Maria Grazia GasparoUniversita degli Studi di [email protected]

Ricardo NanculefFederico Santa Maria Technical [email protected]

Alessandra PapiniUniversita degli Studi di [email protected]

PP1

Efficient Simulation and Parameter Estimation fora Biologically Inspired Bipedal Robot

A multi-body systems dynamics model for a bipedal robotwhose legs are actuated by eight series-elastic structuresapproximating the main human leg muscle groups is de-veloped allowing automated differentiation with respect tomodel parameters. Based on the dynamics model a tailoreddirect multiple shooting approach is applied for estimationof unknown parameters based on measurements from well

162 OP11 Abstracts

defined independent experiments of the real robot.

Christian Reinl, Martin Friedmann, Dorian ScholzTechnische Universitat [email protected],[email protected],[email protected]


PP1

Robust Optimization Problems with Sums of Max-ima of Linear Functions

The sum of maxima of linear functions plays an importantrole in LP models for inventory management, supply chainmanagement, regression models, tumour treatment, andmany other practical problems. In the literature, often thewrong robust counterpart is used. We present new methodsfor dealing with the correct robust counterpart:∑

i∈I

maxj∈J

{�i,j(ζ, x)} ≤ d ∀ζ ∈ Z,

where �i,j is a bi-affine function. We apply our methodsto toy and practical problems, and indeed find that oftenlyused methods lead to inferior solutions.

Bram Gorissen, Dick HertogTilburg UniversityTilburg, The [email protected], [email protected]

PP1

Geometry Optimization of Branched Sheet MetalProducts

We consider the geometry optimization of hydroformedbranched sheet metal products which are produced usingthe technology of linear flow splitting explored in the Col-laborative Research Center 666. We present the associatedproblem for optimizing the stiffness of the structure with3D linear elasticity equations as constraints. Then an algo-rithm for solving this problem using exact constraints anda globalization strategy based on adaptive cubic regular-ization is presented. Numerical results for an example aregiven.

Thea Gollner, Wolfgang Hess, Stefan UlbrichTU [email protected],[email protected], [email protected]

PP1

On Some Strange Properties in Rank MinimizationProblems

Consider a rank minimization problem:

(P)

{Minimize f(A) := rank of Asubject to A ∈ C,

where C is a subset of M,\(R).We state some strange results for problem (P).

• Every admissible point in (P) is a local minimizer.

• The Moreau-Yosida regularized form and the proxi-mal mapping associated with the rank function canbe explicitly calculated.

• For k ∈ {0, 1, . . . , p} and r ≥ 0, let

Srk := {M ∈ M,\(R)| rank M ≤ ∇ and ‖M‖∫√ ≤ ∇}.

Then

co Srk = {M ∈ M,\(R)| ‖M‖∫√ ≤ ∇ and ‖M‖∗ ≤ ∇‖}.

• The generalized subdifferentials of the rank functionall coincide and the common value is a vector spaceof M,\(R)

Le Hai YenPh.D [email protected]

Jean-Baptiste Hiriart-UrrutyUniversity of [email protected]

PP1

Selection of Securitization Baskets with Consider-ation of Conditional Value-at-Risk and ExpectedReturns

Financial institutes use structured products for transfer-ring risk (Conditional Value-at-Risk) arising from loan bas-kets. Arranging the basket for such transactions is a com-plex task often done with naive heuristics being far fromoptimal. The presented approach is based on MINLPs withvarious risk-return objectives. We compare different for-mulations which we transform into MILPs according toRockafellar and Uryasev. We give numerical examples us-ing a Merton’s type portfolio model and Monte-Carlo sim-ulation with Glasserman’s Importance Sampling.

Matthias HeidrichTechnische UniversitFachbereich [email protected]


PP1

Sensitivity Analysis and Parameter EstimationMethods for Models of Complex Biological Pro-cesses

Mathematical models of complex biological processes re-quire numerical methods for quantitative analysis, wheresensitivity analysis and parameter estimation play a cru-cial role. Especially interesting is reverse sensitivity analy-sis which allow to determine which model data have whatinfluence on a selected model output and thus to identifymodel structures.We present sensitivity analysis and parameter estimationmethods for models of reaction-diffusion equations. Themethods are successfully applied in modelling of Min-system oscillations in Escherichia coli.

Alexandra G. Herzog

OP11 Abstracts 163

Dep. of Mathematics and Computer Science, Univ. [email protected]

Jens Herwig, Tanja Binder, Max NattermannDep. of Mathematics and Computer Science,University of [email protected],[email protected],[email protected]

Ekaterina KostinaFachbereich Mathematik und InformatikPhilipps-Universitaet [email protected]

PP1

Alternating-Direction Optimization with Mas-sively Parallel Trust-Regions for Partially Separa-ble Non-Linear Objectives

Large inverse problems consisting of a separable fidelityterm and non-separable regularization term(s) can be ad-dressed through the ADMM method. Recent methods(like Chambolles) can address the regularization term.The fidelity minimization then becomes a large number(sometimes millions) of low-dimensional independent sub-problems. For vector-valued data, these sub-problems maythemselves be multi-dimensional. When highly nonlinear,these can be solved in lock-step parallel using damped trustregions, which are particularly well suited for GPU imple-mentation.

Kevin M. HoltVarian Medical [email protected]

PP1

Numerical Solution of a Conspicuous ConsumptionModel with Constant Control Delay

We derive optimal pricing strategies for conspicuous con-sumption products in recession periods. We investigatea two-stage economic optimal control problem, includinguncertainty of the recession length and delay effects of thepricing strategy. We propose a structure-exploiting directmethod for optimal control, targeting uncertainties by sce-nario trees and control delays by slack control functions.Numerical results illustrate the validity of our approachand show the impact of uncertainties and delay effects onoptimal economic strategies.

Tony HuschtoInterdisciplinary Center for Scientific Computing,Heidelberg [email protected]

Gustav FeichtingerInstitute for Mathematical Methods in EconomicsVienna University of [email protected]

Richard HartlDepartment of Business AdministrationUniversity of [email protected]

Peter Kort

Department of Econometrics & Operations Research andCentERTilburg [email protected]


Andrea SeidlInstitute for Mathematical Methods in EconomicsVienna University of [email protected]

PP1

Coupling Edges in Graph Cuts

We study a new graph cut problem, cooperative cut, wherethe cost is a submodular function on sets of edges. The re-sulting coupling of edges allows novel applications, e.g., im-proving image segmentation by favoring congruous bound-aries. It also generalizes some recent models in computervision. Such expressive power comes at the price of a lowerbound on the approximation factor. However, we also showhow to find good solutions with bounded approximationfactors.

Stefanie JegelkaMax Planck for Biological [email protected]

Jeff BilmesUniversity of [email protected]

PP1

The Integral Approximation Problem for Mixed-Integer Nonlinear Optimal Control

We propose a decomposition approach for Mixed Inte-ger Nonlinear Optimal Control Problems (MIOCPs). TheMIOCP is decomposed into a relaxed continuous one and aMILP to find values for integer control functions. We dis-cuss the connection of optimal solutions to sum up round-ing solutions, tailored Branch-and-Bound algorithms andLagrangian relaxations. We provide an upper bound onthe distance between the optimal MIOCP objective andthe one found by our computationally efficient decomposi-tion approach.

Michael JungIWR [email protected]


Gerhard ReineltIWR, University of [email protected]

PP1

Decentralized Model-Predictive Control for Au-tonomous Vehicles in Cooperative Missions

For a scenario from environmental monitoring, a decentral-

164 OP11 Abstracts

ized approach for optimal cooperative control of heteroge-neous multi-vehicle systems is investigated. It is demon-strated that using approximated motion dynamics and amodel-predictive control method based on MILP, optimalcontrol inputs can be computed in real-time. By employingan adaptive sampling strategy, the hybrid control problemis linked to an identification problem for the estimation andprediction of a dispersal process of airborne contaminants.

Juliane KuhnSimulation, Systems Optimization, and Robotics GroupDepartment of Computer Science, TU [email protected]


PP1

Optimal Deceleration of Rotation of a SymmetricBody with Internal Degrees of Freedom in a Resis-tive Medium

The problem of time-optimal deceleration of rotation ofdynamically symmetric body is studied. It is assumed thatthe body contains a cavity filled with viscous liquid and amass connected to the body by coupling with square-lowdissipation. Deceleration moment of viscous friction forcesacts on the body. The optimal control law for decelerationof rotation in the form of synthesis, the operation time andthe phase trajectories are determined.

Dmytro D. LeshchenkoOdessa State Academy of Civil Engineering andArchitectureleshchenko [email protected]

Leonid D. AkulenkoInstitute for Problems in Mechanics [email protected]

Yanina S. Zinkevich, Alla L. RachinskayaOdessa State Academy of Civil Engineering [email protected], [email protected]

PP1

Low Multilinear Rank Tensor Decomposition ViaSingular Value Thresholding

We present a new numerical method for tensor dimension-ality reduction. The method is based on the tensor traceclass norm which allows an optimization formulation foreach tensor mode for finding the best low multilinear ranktensor approximation. By using singular value threshold-ing (SVT) technique, the method is implemented itera-tively to obtain low rank factor in each mode. Some nu-merical examples illustrate the efficiency and accuracy ofour method.

Na LiClarkson UniversityDept. of [email protected]

Carmeliza NavascaClarkson [email protected]

PP1

Graph Partitioning and Applications

Applications of graph partitioning problems abound in dif-ferent areas,among them in theoretical physics and in VLSIlayout. In this poster, we introduce exact approaches forsolving graph partitioning problems together with resultsfor the applications.

Frauke LiersInstitut fur InformatikUniversitat zu [email protected]

PP1

A Frechet Differentiability Result for Shape Opti-mization with Instationary Navier-Stokes Flow

We consider shape optimization problems where an objectis exposed to instationary Navier-Stokes flow. Assumingthe data are sufficiently smooth we show Frechet differ-entiability of the velocity with respect to W 2,∞ domainvariations in 2D/3D. Here, the handling of the incompress-ibility condition and the low time regularity of the pressureplay a crucial role in the analysis. Furthermore, we presentnumerical results using an adjoint-based approach for cal-culating the shape derivatives.

Florian LindemannTechnische Universitaet [email protected]



Christian BrandenburgTU [email protected]

PP1

Recursive Formulation of Limited Memory Vari-able Metric Methods

We propose a new recursive matrix formulation of limitedmemory variable metric methods. This approach enablesto approximate both the Hessian matrix and its inverseand can be used for an arbitrary update from the Broy-den class. The new recursive formulation requires approxi-mately 4mn multiplications and additions for the directiondetermination.

Ladislav Luksan, Jan VlcekInstitute of Computer ScienceAcademy of Sciences of the Czech [email protected], [email protected]

PP1

Recursive Formulation of Limited Memory Vari-

OP11 Abstracts 165

able Metric Methods

In this contribution, we propose a new recursive matrixformulation of limited memory variable metric methods.This approach can be used for an arbitrary update from theBroyden class (and some other updates) and also for theapproximation of both the Hessian matrix and its inverse.The new recursive formulation requires approximately 4mnmultiplications and additions per iteration, so it is compa-rable with other efficient limited memory variable metricmethods. Numerical experiments concerning Algorithm 1,proposed in this report, confirm its practical efficiency.

Ladislav Luksan, Jan VlcekInstitute of Computer ScienceAcademy of Sciences of the Czech [email protected], [email protected]

PP1

The Use of Influenza Vaccination Strategies WhenSupply Is Limited

The 2009 A (H1N1) influenza pandemic was rather atypi-cal. The world’s limited capacity to produce an adequatevaccine supply over just a few months resulted in the de-velopment of public health policies that “had” to optimizethe utilization of limited vaccine supplies. We use optimalcontrol theory to explore the impact of some of the con-straints faced by most nations in implementing a publichealth policy that tried to meet the challenges that comefrom having access only to a limited vaccine supply that isnever 100% effective.

Romarie MoralesArizona State [email protected]

Sunmi LeeMathematical, Computational and Modeling SciencesCenter,Arizona State University,[email protected]

Carlos Castillo ChavezArizona State [email protected]

PP1

Dynamic Modeling and Optimal Control for Indus-trial Robots in Milling Applications

The application of industrial robots for milling tasks resultsin high process forces at the end effector which lead to pathdeviations caused by joint elasticities. A coupled simula-tion model of robot dynamics and its interaction with themilling process is based on an extended rigid multi-bodydescription incorporating joint elasticities and tilting ef-fects. The implementation of automatic differentiation en-ables computation of compensation trajectories by directoptimal control methods.

Christian Reinl, Martin Friedmann, Elmar BrendelTechnische Universitat [email protected],[email protected],[email protected]

Oskar Von StrykDepartment of Computer Science

Technische Universitat [email protected]

PP1

A Randomized Coordinate Descent Method forLarge-Scale Truss Topology Design

We develop a randomized coordinate descent method forminimizing the sum of a smooth and a simple nonsmoothseparable convex function and prove that the method ob-tains an ε-accurate solution with probability at least 1 − ρin at most O((n/ε) log(n/ερ)) iterations, where n is the di-mension of the problem. This simplifies, improves and ex-tends recent results of Nesterov [2/2010]. It appears thatthe method is suitable for solving large-scale truss topologydesign problems.

Peter Richtarik, Martin TakacUniversity of [email protected], [email protected]

PP1

Piecewise Monotonic Regression Algorithm forProblems Comprising Seasonal and MonotonicTrends

In this research piecewise monotonic models for problemscomprising seasonal cycles and monotonic trends are con-sidered. In contrast to the conventional piecewise mono-tonic regression algorithms, our approach can efficientlyexploit a priori information about temporal patterns. Itis based on reducing these problems to monotonic regres-sion problems defined on partially ordered data sets. Thelatter are large-scale convex quadratic programming prob-lems. They are efficiently solved by the GPAV algorithm.

Amirhossein SadoghiDepartment of Computer ScienceLinkoping [email protected]


Anders GrimvallDepartment of Computer ScienceLinkoping University,[email protected]

PP1

An Infeasible-Point Subgradient Method UsingApproximate Projections

We introduce a subgradient algorithm which applies inex-act projections and thus is not required to maintain feasi-bility of the iterates throughout the algorithmic progress.We prove its convergence under reasonable conditions,investigating two classical step size schemes. We alsopresent computational results from an application to �1-minimization (Basis Pursuit) as commonly considered incompressed sensing. Here, projection inaccuracies arecaused by a truncated CG method which is applied to solvethe projection subproblems.

Andreas M. TillmannTechnische Universitat Braunschweig

166 OP11 Abstracts

[email protected]

Dirk Lorenz, Marc PfetschTU [email protected], [email protected]

PP1

Robust Markov Decision Processes

Markov decision processes (MDPs) are powerful tools fordecision making in uncertain dynamic environments. How-ever, the solutions of MDPs are of limited practical usedue to their sensitivity to distributional model parame-ters, which are typically unknown and have to be estimatedby the decision maker. To counter the detrimental effectsof estimation errors, we consider robust MDPs that offerprobabilistic guarantees in view of the unknown parame-ters. To this end, we assume that an observation historyof the MDP is available. Based on this history, we derivea confidence region that contains the unknown parame-ters with a pre-specified probability 1− β. Afterwards, wedetermine a policy that attains the highest worst-case per-formance over this confidence region. By construction, thispolicy achieves or exceeds its worst-case performance witha confidence of at least 1 − β. Our method involves thesolution of tractable conic programs of moderate size.

Wolfram WiesemannDepartment of ComputingImperial College [email protected]

Daniel Kuhn, Berc RustemImperial College [email protected], [email protected]

PP1

Robust Optimization Using Historical Data

We provide a robust solution approach for linear optimiza-tion problems with uncertain parameters. Only historicaldata on the uncertain parameters is used in order to con-struct the uncertainty set. The aim is to find the tightestuncertainty set such that the constraints of the problemare satisfied with at least a given probability. This ap-proach yields tighter uncertainty regions than the standardapproach, and moreover does not require independency ofthe uncertain parameters.

Ihsan YanikogluDepartment of Econometrics and OR,Tilburg [email protected]

Dick den HertogUniversity of TilburgThe [email protected]

Goos KantTilburg [email protected]

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OP11 Abstracts - Society for Industrial and Applied ... · 72 OP11 Abstracts certain loads. We present the implementation of the opti-mal positioning of active components within a