70 OP11 Abstracts

IP1 general. Moreover, box constraints on the state function Sparse Optimization are also admitted. Later, the model is improved by including Maxwell equations for induction heating and state Many computational problems of recent interest can be constraints on the generated temperature. Also the com- formulated as optimization problems that contain an un- pletion of the model by Navier-Stokes equations in a melt is derlying objective together with regularization terms that briefly mentioned. For these problems, the well-posedness promote a particular type of structure in the solution. of the underlying systems of PDEs and the principal form Since a commonly desired property is that the vector of of optimality conditions are sketched. Numerical examples unknowns should have relatively few nonzeros (a “sparse illustrate the theory, justify certain simplifications and and vector’), the term “sparse optimization’ is used as a broad motivate the necessity of more complex models. Finally, label for the area. These problems have arisen in machine ongoing research on applications to industrial processes of learning, image processing, compressed sensing, and sev- crystal growth is briefly addressed. eral other fields. This talk surveys several applications that can be formulated and solved as sparse optimization Fredi Tröltzsch problems, highlighting the novel ways in which algorithms Technische Universität, Berlin have been assembled from a wide variety of optimization [email protected] techniques, old and new. Stephen Wright IP4 University of Wisconsin Matrix Optimization: Searching Between the First Dept. of Computer Sciences andSecondOrderMethods [email protected] During the last two decades, matrix optimization problems (MOPs) have undergone rapid developments due to IP2 their wide applications as well as their mathematical ele- Optimizing Radiation Therapy - Past Accomplish- gance. In the early days, second order methods, in par- ments and Future Challenges ticular the interior point methods (IPMs), seemed to be a natural choice for solving MOPs. This choice has been Optimization has found a successful and broad application perfectly justified over the years by the success of using in intensity-modulated radiation therapy (IMRT). We will IPMs to solve small and medium sized semi-definite pro- briefly review the standard model of IMRT optimization. gramming (SDP) problems. On the other hand, since at There is still a lot of space for improvement in IMRT and each iteration the memory requirement and the computa- elsewhere in radiation therapy: 1. Optimization of the tional cost for second order methods grow too fast with irradiation geometry including multiple fixed beams and the number of constraints and the matrix dimensions in dynamic arcs. 2. The adaptation (re-optimization) of the MOPs, second order methods have recently become less treatment during the course of treatment. 3. The han- popular. The current trend is to apply first order methods dling of motion and uncertainties, particularly in proton to MOPs. This comes no surprise as first order methods therapy, and 4. The direct optimization of treatment out- normally need less computational cost at each iteration. come rather than physical (dosimetric) surrogates of it. A To say the least while first order methods can often run for general challenge is that physicians often cannot provide some iterations even for large scale problems, the second clear mathematical objectives and strict constraints. In- order methods may fail even at the first iteration. However, stead, they pursue an I know it when I see it approach. We for many MOPs the overall cost of first order methods for try to address this issue through interactive multi-criteria obtaining a reasonably good solution is often prohibitive, optimization. if possible at all. To break this deadlock, we need to construct algorithms that possess two desirable properties: 1) Thomas Bortfeld at each iteration the computational cost is affordable; and Massachusetts General Hospital and Harvard Medical 2) the convergence speed is fast but may not be as fast School as second order methods (no free lunch). In this talk, by Department of Radiation Oncology using least squares correlation matrix and SDP problems [email protected] as examples we demonstrate how these two properties can be potentially achieved simultaneously. Variational analysis, in particular semi-smooth analysis, will be empha- IP3 sized and inexact proximal point algorithms (PPAs) will be On Some Optimal Control Problems of Electro- recommended for solving large scale symmetric and non- magnetic Fields symmetric MOPs.

In this survey, a sequence of optimal control problems for Defeng Sun systems of partial differential equations of increasing com- Dept of Mathematics plexity is discussed. The audience is guided step by step National University of Singapore from an academic heating problem to fairly complex con- [email protected] trol problems of induction heating. While the first problem is modeled by the Poission equation, the last one is related to industrial applications. It includes equations for IP5 heat conduction, heat radiation, and Maxwell equations Replacing Spectral Techniques for Expander Ratio, modeling induction heating. To introduce into main prin- Normalized Cut and Conductance by Combinato- ciples of PDE control, the talk begins with a simplified rial Flow Algorithms optimal control problem for a linear elliptic equation with box constraints on the control function. It can be inter- We address challenging problems in clustering, partition- preted as a heating problem. Next, nonlinear local and ing and imaging including the normalized cut problem, nonlocal radiation boundary conditions are considered and graph expander, Cheeger constant problem and conduc- the geometry of the computational domain will be more tance problem. These have traditionally been solved using OP11 Abstracts 71

the “spectral technique”. These problems are formulated IP8 here as a quadratic ratio (Raleigh) with discrete constraints Title Not Available at Time of Publication and a single sum constraint. The spectral method solves a relaxation that omits the discreteness constraints. A new Abstract not available at time of publication. relaxation, that omits the sum constraint, is shown to be solvable in strongly polynomial time. It is shown, via an Thomas F. Coleman experimental study, that the results of the combinatorial The Ophelia Lazaridis Research Chair algorithm often improve dramatically on the quality of the University of Waterloo results of the spectral method in image segmentation and [email protected] image denoising instances. Dorit Hochbaum CP1 Industrial Engineering and Operations Research Chance-Constrained Second-Order Cone Program- University of California, Berkeley ming: A Definition [email protected] Second-order cone programs (SOCPs) are class of convex optimization problems. Stochastic SOCPs have been IP6 defined recently to handle uncertainty in data defining Nonsmooth Optimization: Thinking Outside of the SOCPs. A prominent alternative for stochastic program- Black Box ming for handling uncertain data is chance constrained programming (CCP). In this presentation, we introduce In many optimization problems, nonsmoothness appears an extension of CCPs termed chance-constrained second- in a structured manner, because the objective function has order cone programs (CCSOCPs) for handling uncertainty some special form. For example, in compressed sensing, in data defining SOCPs. Some applications of this new regularized least square problems have composite objective paradigm of CCP will be described. functions. Likewise, separable functions arise in large-scale stochastic or mixed-integer programming problems solved Baha M. Alzalg,AriAriyawansa by some decomposition technique. The last decade has Washington State University seen the advent of a new generation of bundle methods, [email protected], [email protected] 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 on CP1 how much data is given by the black box. If certain first- On Semidefinite Programming Relaxations of Max- order information is missing, it is possible to deal with imum K-Section inexactness very efficiently. But if some second-order information is available, it is possible to mimic a Newton We derive a semidefinite programming bound for max k- algorithm and converge rapidly. We outline basic ideas equipartition problem, which is, for k =2,atleastas strong as the well-known bound by Frieze and Jerrum. For and computational questions, highlighting the main fea- ≥ tures and challenges in the area on application examples. k 3 this new bound dominates a bound of Karish and Rendl [S.E. Karish, F. Rendl. Semidefinite Programming and Graph Equipartition. In: Topics in Semidefinite and Claudia Sagastizábal Interior-Point Methods, P.M. Pardalos and H. Wolkowicz, CEPEL Eds., 1998.] The new bound coincides with a recent bound [email protected] by De Klerk and Sotirov for the more general quadratic assignment problem.

IP7 Cristian Dobre Nonlinear Integer Optimization: Incomputability, TiUniversity of Groningen Computability and Computation Groningen, The Netherlands C.Dobre@uvt.nl Within the realm of optimization, the Nonlinear Integer Optimization problem is, in some sense, the mother of all Etienne De Klerk deterministic optimization problems. As such, in its most Tilburg University general form, it is hopelessly intractable. Yet, because of [email protected] its obviously broad scope, it has its allure. By looking at structured yet broad subclasses, interesting and useful Dmitrii Pasechnik results emerge. I will present several results that expand NTU Singapore on its intractability. Looking at these results optimisti- [email protected] cally, we are guided toward directions that can be fruitful for positive results for theory and computation. I will go Renata Sotirov into a lot of detail on combinatorial structures and types of Tilburg University functions for which we have polynomial-time exact and ap- [email protected] proximation algorithms. Finally, I will present the status of some eﬀorts to develop rather “general-purpose’ computational tools (bearing in mind that the general problem is CP1 provably intractable). Robust Design of Active Trusses Via Mixed Integer Jon Lee Semideﬁnite Programming IBM T.J. Watson Research Center This work is an extension of Ben-Tal and Nemirovskis ap- [email protected] 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- of less than 1A.˚ mal positioning of active components within a semidefinite model for robust truss-topology design using binary vari- Xingyuan Fang ables. Different robust approaches (polyhedral and ellip- Princeton University soidal uncertainty sets), solution methods (e.g. cascading [email protected] techniques, projection approaches) and numerical results will be presented. Kim-Chuan Toh National University of Singapore Kai Habermehl Department of Mathematics and Singapore-MIT Alliance TU Darmstadt, Department of Mathematics [email protected] Nonlinear Optimization [email protected] CP1 Stefan Ulbrich Optimization over the Doubly Nonnegative Cone Technische Universitaet Darmstadt Fachbereich Mathematik We often see that each element of the semidefinite relax- [email protected] ation matrix is meant to be nonnegative. Such a matrix is called a doubly nonnegative matrix. In this talk, we will Sonja Friedrich show that the doubly nonnegative relaxation gives signif- TU Darmstadt, Department of Mathematics icantly tight bounds for a class of quadratic assignment Discrete Optimiation problems. We also provide some basic properties of the [email protected] doubly nonnegative cone aiming to develop new and efficient algorithms for solving the doubly nonnegative optimization problems. CP1 Yasuaki Matsukawa Distributionally Robust Optimization and Its Graduate School of Systems and Information Engineering Tractable Approximations University of Tsukuba We focus on a linear optimization problem with uncertain- [email protected] ties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an Akiko Yoshise approximate solution to the problem that is distribution- University of Tsukuba ally robust and more flexible than the standard technique raduate School of Systems and Information Engineering of using linear rules. We convert the uncertain linear pro- [email protected] gram into a deterministic convex program by constructing distributionally robust bounds on these expectations. CP2 Melvyn Sim On Maximally Violated Cuts Obtained from a Ba- NUS Business School sis [email protected] Most cuts used in practice can be derived from a basis and T ≥ Joel Goh are of the form α x 1, where x is a vector of non-basic variables and α ≥ 0. Such cuts are called maximally vio- Stanford University ≥ T [email protected] lated wrt. a pointx ¯ 0ifα x¯ = 0. In an earlier paper we presented computational results for maximally violated cuts derived from an optimal basis of the linear relaxation. CP1 In this talk we also consider pivoting and deriving maxi- Attacking Molecular Conformation Problem by mally violated cuts from alternative non-optimal bases. SDP Kent Andersen We present an improvement of the DISCO algorithm of Le- University of Aarhus ung and Toh for molecular conformation. In the algorithm, [email protected] the recursive steps recursively divide large group of atoms into two overlapping subgroups until each subgroups is suf- CP2 ficient small. At that point, the graph realization problems in the basis steps are solved via semidefinite programs. Af- A New Feasibility Pump-Like Heuristic for Mixed ter which, the subgroups are stitched back together using Integer Problems the overlapping atoms, and the stitched configurations are Mixed-Integer optimization represents a powerful tool for refined by a gradient decent method. We use chemical in- modeling many optimization problems arising from real- formation such as bond lengths and angles for atoms on world applications. The Feasibility pump is a heuristic for the backbone of a protein molecule to improve the robust- finding feasible solutions to mixed integer linear problems. ness of the DISCO algorithm for computing the structure In this work, we propose a new feasibility pump approach of a protein molecule given only a very sparse subset (20%) using concave non differentiable penalty functions for mea- of inter-atomic distances that are less than 6Aand˚ are cor- suring solution integrality. We present computational re- rupted by high level of noise. Tests on molecules taken from sults on general MILP problems from the MIPLIB library the Protein Data Bank show that our improved algorithm showing the effectiveness of our approach. is able to reliably and efficiently reconstruct the conformation of large molecules. For instance, a 6000-atom confor- Marianna De Santis, Stefano Lucidi, Francesco Rinaldi mation problem is solved within an hour with an RMSD University of Rome [email protected], [email protected], OP11 Abstracts 73

[email protected] based on the proposed reformulations, and we present computational results on binary MILP problems showing the usefulness of the approach. CP2 A Traveling Salesman Problem with Quadratic Francesco Rinaldi, Marianna De Santis Cost Structure University of Rome [email protected], [email protected] We regard a traveling salesman problem with quadratic cost terms (QTSP) depending on any two successive arcs in the tour. This problem is motivated by an application CP2 in bioinformatics – the recognition of transcription factor Orbital Branching for Quadratic Assignment Prob- binding sites in gene regulation. It can also be used to lems of High Symmetry solve the angular-metric traveling salesman problem ap- pearing in connection with robotics and traveling sales- Quadratic assignment problems are notoriously difficult man problems with reload costs. For the linearized QTSP to solve to optimality, and the difficulties are often com- model we present a polyhedral study and investigate the pounded in instances exhibiting a high degree of symmetry computational complexity of the corresponding separation among decision variables. To address symmetry, we pro- problems. Using the new cuts, real world instances from pose an orbital-branching approach geared specially toward biology can be solved up to 80 cities in less than 13 min- quadratic assignment problems. utes. Random instances turn out to be difficult, but on these semidefinite relaxations help to reduce the gap in the Stephen E. Wright root node significantly. Miami University Dept of Math & Statistics Anja Fischer, Christoph Helmberg [email protected] Chemnitz University of Technology anja.fi[email protected], [email protected] CP3 Adjoint-Based Global Error Techniques for Inte- gration in Optimal Control Problems CP2 A Novel Model: Planning, Scheduling and Re- Using the direct multiple shooting method to solve opti- source Allocation of Engineering Activities in Man- mal control problems requires integrating dynamical sys- ufacturing Systems and Service Industries tems and generating sensitivity information for function and derivative evaluation. To do this efficiently, discretiza- This research deals with planning, scheduling and resource tion schemes should be chosen to balance accuracy require- allocation of activities in non-shop floor areas of manu- ments for a successful optimization against computational facturing systems and service industries. A mixed integer effort. To this end we investigate global error techniques programming model and a decision support system was de- based on adjoint information. We present how this ad- veloped, including operational features such as flexibility joint information can efficiently be obtained from quanti- of work force, legal restrictions on workload, and acces- ties computed by backward differentiation of the integra- sible capacities and resources. A real-life test, originating tion scheme in the case of variable-stepsize, variable-order from an industrial partner, shows the flexibility and the ro- BDF methods. bustness of the model by solving planning and scheduling problems. Doerte Beigel Interdisciplinary Center for Scientific Computing (IWR) Yousef Hooshmand Heidelberg University Institute for Product Engineering [email protected] University of Duisburg-Essen, Germany [email protected] Hans Georg Bock IWR, University of Heidelberg Amir Hooshmand [email protected] Institute for Advanced Study Technical University of Munich, Germany Johannes Schloeder [email protected] IWR, University of Heidelberg, Germany [email protected] Dalibor Dudic Stuttgart University Germany CP3 [email protected] Symmetric Error Estimates for Discontinuous Time Stepping Schemes for Optimal Control Prob- lems CP2 New Continuous Reformulations for Zero-One Pro- A discontinuous Galerkin finite element method for an op- gramming Problems timal control problem having states constrained to linear and semi-linear parabolic PDE’s is examined. The schemes In this work, we study continuous reformulations of zero- under consideration are discontinuous in time but conform- one programming problems. We prove that, under suitable ing in space. We present some results concerning error es- conditions, the optimal solutions of a zero-one program- timates for the first order necessary conditions under min- ming problem can be obtained by solving a specific contin- imal regularity assumptions. The estimates are of sym- uous problem. Furthermore, we develop a new feasibility- metric type and lead to optimal convergence rates under pump like approach for zero-one programming problems 74 OP11 Abstracts

suitable assumptions on the data. particular, linear approximations are used for reasons of efficiency and global optimality of the resulting mixed- Konstantinos Chrysafinos integer linear problem. For benchmark scenarios and for Department of Mathematics new problems numerical results are demonstrating real- National Technical University of Athens, Greece time competitiveness as well as limitations. chrysafi[email protected] Christian Reinl Technische Universität Darmstadt CP3 [email protected] Convex Optimization for Model Predictive Control Oskar Von Stryk In this contribution, we describe algorithms and computa- Department of Computer Science tional performance of quadratic programming algorithms Technische Universität Darmstadt tailored for linear MPC with soft output constraints. We [email protected] consider a primal active-set algorithm, a dual-active set algorithm, and a primal-dual interior-point algorithm for solution of convex QPs and tailor these algorithms for CP3 the special structure of linear MPC with soft output con- Experiments of Automatic Differentiation in straints. Linear MPC with soft output constraints is an Aerospace Applications attractive optimization model for control of uncertain linear systems and systems with asymmetric penalty func- EADS Innovation Works, as research center of EADS, is tions. However, the size of the decision variables grows involved in the development of inverse methods for trajec- with the number of soft output constraints and slack vari- tory tools. Two aerospace applications will be presented ables introduced to shape the penalty function for the MPC with a focus on inverse problem, optimal control and first problem. The resulting convex QP for the linear MPC with experiments with automatic differentiation (AD): 1. Iden- soft constraints easily becomes much larger than the equiv- tification of aerodynamics coefficients of a probe for differ- alent linear MPC without soft output constraints. Due to ent flight conditions given trajectories measurements. The the real-time computational requirement off-the-shelf QP industrial objective is to design space vehicles having an algorithms are often too slow and efficient convex QP al- accurate stability. 2. Identification of heat flux coefficients gorithms tailored for this problem are needed. from time domain temperature measurements. The industrial objective is the dimensioning of thermal protection John B. Jorgensen system for atmospheric re-entry missions of aerospace vehi- DTU Informatics cles. For these two applications, the inverse problem is also Technical University of Denmark formulated as a minimization problem with optimal con- [email protected] trol formulation (lagrangian, adjoint and gradients computations and connected to an optimization loop). First CP3 encouraging results of automatic differentiation procedure on these industrial applications will be presented, with val- A Total Site Optimization Study for Plantwide idations in agreement with measurements Control Stéphane alestra, Vassili Srithammavanh In order to develop control strategies for entire plants EADS INNOVATION WORKS (plantwide control) and to jump over the lack of algorithms [email protected], that is still present in this field we can apply total site [email protected] steady-state optimization and then select the best control strategy. This paper is presenting a study of a total site optimization for a vacuum residue processing plant in or- CP4 der to maximize profit. The results will then be used as a Approximating the Solution Set in Multi-Criteria priori information in the development of control strategies Radiation Therapy Optimization for the same plant. Optimal planning of a radiation therapy treatment is a Ionut Muntean, Andreea Savu, Gheorghe Lazea, Mihail multi-criteria decision problem due to the conflict between Abrudean tumor dose and sparing of healthy tissue. An algorithm for Technical University of Cluj-Napoca, Faculty of generating a set of treatment plans such that these consti- Automation tute a representative approximation of the solution set to and Computer Science, Automation Department this problem is considered. We provide a dual formulation [email protected], of the algorithm that improves its computational complex- [email protected], [email protected], ity, thus extending the range of treatment cases to which [email protected] the algorithm is amenable. Rasmus Bokrantz CP3 Royal Institute of Technology, Stockholm Trajectory Planning and Task Allocation of Co- Raysearch Laboratories operating Vehicles Based on Discrete-Continuous [email protected] Modeling and Optimization Optimal task allocation and trajectory planning for coop- Anders Forsgren erating vehicles is characterized by complex multi-phase Royal Institute of Technology (KTH) control problems with tight coupling of discrete structure Dept. of Mathematics and continuous dynamics. Using hierarchical hybrid au- [email protected] tomata and applying appropriate transformations, makes the model accessible for mathematical optimization. In OP11 Abstracts 75

CP4 vantage of this technology. We propose some exact and Robust Optimization for Proton Therapy Treat- heuristic approaches, and present results on real patient ment Planning data. Proton therapy is sensitive to errors such as patient mis- Marina A. Epelman, Fei Peng, Edwin Romeijn alignments and incorrect treatment volume densities. Fail- University of Michigan ing to account for uncertainties may compromise the treat- Industrial and Operations Engineering ment plan quality drastically. By utilizing information [email protected], fei peng ¡[email protected]¿, about the uncertainties and performing minimax optimiza- [email protected] tions, we achieve robust treatment plans. We show that these plans provide more robustness and better sparing of healthy tissues than those of conventional methods for CP4 robustness, such as using margins and enforcing uniform An Inexact Algorithm in Function Space for Opti- beam doses. mization with Non-Linear Pdes Albin Fredriksson We consider an algorithm for non-linear equality con- Royal Institute of Technoloy, Stockholm strained optimization in function space, which is taylored RaySearch Laboratories, Stockholm for optimization problems with non-linear PDEs. The al- [email protected] gorithm computes inexact steps in function space, where inexactness arises from the discretization of a PDE. Dis- Anders Forsgren cretization errors are controlled by an a-posteriori error Royal Institute of Technology (KTH) estimation and adaptive grid refinement. As an applica- Dept. of Mathematics tion we present a problem from medical therapy planning. [email protected] Anton Schiela Björn H˚ardemark ZIB, Berlin RaySearch Laboratories, Stockholm [email protected] [email protected] Martin Weiser CP4 Zuse Institute (ZIB) Berlin, Germany A Mathematical Model for Increasing the Effec- [email protected] tiveness of the Treatment of Cancer Patients

A stochastic model is developed to describe the growth of CP4 heterogenous tumor for dispersed cell regime. The mathematical model is non-linear stochastic partial differential Optimization of Freezing and Thawing Protocols equation with a multiplicative colored noise term in the for Reduction of Injuring Effects of Cryopreserva- three dimensional space. The main feature of the model tion is that it takes into account random interactions between Mathematical models of ice formation inside and outside tumor cells, immune system cells, and ati-cancer drugs. of living cells during freezing and thawing are derived by The existence of weak solutions, pathwise uniqueness and applying an appropriate averaging technique to partial dif- the convergence in probability of the approzimated solu- ferential equations describing the dynamics of water-to-ice tions to the exact solution of the stochastic problem are phase change. This reduces spatially distributed relations established. Some applications are suggested. The math- to a few ordinary differential equations with control pa- ematical results of the study make possible the construc- rameters and uncertainties. Additionally, state constraints tion of computer programs and simulations for predicting are introduced to avoid the excessive heating of cells. The the effect of chemotherapy, immunotherapy or genether- obtained equations together with an appropriate objective apy for each patient. The main idea of this study is: tak- functional that expresses some injuring effects of cell freezing into consideration the biomedical parameters of each ing or thawing are considered as a conflict-controlled prob- patient and the computer simulations for chemotherapy, lem where the aim of the control is to minimize the objec- immunotherapy or genetherapy, it will support and assist tive functional, and the aim of the disturbance is opposite. the medical staff to identify the most effective treatments A stable finite-difference scheme for computing the value for each cancer patient. function of this problem is developed. Using the computed Fejzi Kolaneci value function, optimized cooling and thawing protocols University of New York, Tirana are designed. [email protected] Varvara Turova, Nikolai D. Botkin, Karl-Heinz Hoffmann, Natalie Mayer CP4 Technische Universität München, Department of Mathematics Models and Algorithms for Imat and Vmat Arc Chair of Mathematical Modelling Therapy Plan Optimization in Radiation Oncology [email protected], [email protected], In contrast with traditional IMRT, an IMAT or hoff[email protected], [email protected] VMAT machine delivers radiation in a non-stop fashion while the gantry moves continuously during treatment. CP5 IMAT/VMAT machines allow the possibility of delivering high-quality treatments in shorter time than IMRT. How- Selection of Districts for Data Entry Sites in East- ever, their complex settings require new classes of models and algorithms to design treatment plans that take ad- 76 OP11 Abstracts

ern Java Household Census as follows : find the one to one correspondence between two sets of vectors that minimizes the maximal difference Eastern Java has 38 districts and an estimated popula- of the maximum sum and the minumum one. We propose tion size of thirty eight millions. District can be kabu- approximate algorithms that use the searching method for paten or kota such as Kediri, Malang, Pasuruan, if it the balanced assignment problem. is a kabupaten then the word kabupaten is not written. Most economical data entry is achieved with six districts Yuusaku Kamura,MarioNakamori as data entry sites serving Eastern Java , they are 22Bo- Tokyo A&T University jonegoro, 08Kediri, 15Malang, 20Probolinggo, 25kotaSur- [email protected], [email protected] abaya, 35Jember . Since 25kota Surabaya has a short distance to provincial capital, 25kota Surabaya can serve as an alternative to data entry in provincial capital. Under CP5 current plan, provincial capital is preselected as data entry A Distributed Optimization Framework for Maxi- site. This work however is done without such constraint mizing Occupant Comfort in Smart Buildings as preselected provincial capital . This work is minimizing cost by p-median linear programming. Cost includes We propose a distributed optimization framework for max- scanner price and questionnaire delivery cost. imizing the thermal comfort of occupants in a smart building, subject to occupant preferences, HVAC equipment, Rosa Dahlia and energy constraints, by modeling the building as a hi- STIS erarchical, distributed parameter system. We propose dif- pope [email protected] ferent algorithms to decompose the resulting non-convex, constrained optimization problem into subproblems, that are solved by multiple agents. At each timestep, the agents CP5 play a cooperative game and converge to an equilibrium to Risk Aversion in The Newsvendor Problem with decide the optimal values of the building operational vari- Uncertain Supply: CVaR Criterion ables. Our experimental evaluation shows that the coupling among the variables and constraints affects the per- In this presentation, we consider a production firm with formance of the distributed algorithms and that the opti- stochastic yield. We assume the decision maker is risk- mal comfort achieved by the distributed algorithms is com- averse and wants to optimize and control the risk of short- parable to that of the centralized approach. fall. The model is one-period and the decision variables are selling price and the mean of production quantity. The Sudha Krishnamurthy, Arvind Raghunathan decision criterion which is used, is the Conditional Value United Technologies Research Center at Risk(CVaR). [email protected], [email protected]

Saman Eskandarzadeh, Kourosh Eshghi Sharif University of Technology CP5 [email protected], [email protected] Scheduling Algorithm for Sensors on Network

We consider a scheduling algorithm for optical space CP5 surveillance sensors on a network. The algorithm is struc- Dynamic Graph Generation and Asynchronous tured in several stages of approximation using linear pro- Parallel Bundle Methods for Train Timetabling gramming formulation in each stage, such as bin-packing Problems or traveling salesman, to closely approximate an optimal solution. We present results for 1500 satellites over a The Train Timetabling Problem deals with finding conflict 24h scheduling period. Using only one optical sensor, free routes for different trains in a railway network. A tra- the results compare very favorably to an analogous greedy ditional approach uses Lagrangian decomposition of cou- scheduling algorithm. We also present results using 3 op- pling constraints in a network flow model. We develop dy- tical sensors. namic graph generation techniques and asynchronous parallel bundle methods optimizing over dynamically deter- Zoran Spasojevic mined subspaces to handle the very large scale instances Massachusetts Institute of Technology - Lincoln from the railway-network of Deutsche Bahn. Laboratory [email protected] Frank Fischer Chemnitz University of Technology frank.fi[email protected] CP6 Allocation of Maximal Capacities in Gas Networks Christoph Helmberg TU Chemnitz Given a gas network, we search an optimal allocation of ca- Germany pacities for each supply and demand node. An allocation is [email protected] feasible if each request (supply equals demand) is guaranteed to be transportable through the network. We propose an algorithm for solving a reduced variant of the capacity CP5 allocation problem using an MIP relaxation of the original Modified Balanced Assignment Problem in Vector (nonconvex) MINLP transportation problem as black box. Case The suitability of our approach is demonstrated on real-life gas network instances. We extend the well known balanced assignment problem to the case where costs are expressed by m-dimensional Christine Hayn vectors. For the balanced assignment problem, a polyno- University of Erlangen-Nuremberg mial time algorithm has been proposed. Our problem is EDOM OP11 Abstracts 77

[email protected] CP6 A MINLP Primal Heuristic for Gas Networks Lars Schewe Friedrich-Alexander-Universität Erlangen Nürnberg, We consider the problem of stationary optimization in gas Department Mathematik, EDOM networks. The combination of nonlinear gas dynamics to- [email protected] gether with combinatorial aspects of switchable network devices leads to very difficult mixed integer nonlinear opti- Alexander Martin mization problems. We present a MINLP primal heuristic University of Erlangen-Nürnberg that models most of the combinatorial aspects by smooth [email protected] approximations or relaxations and additionally incorpo- rates ODEs of gas dynamics and highly detailed models of active devices. The practicability of our approach is CP6 shownonreal-worldinstances. Topology Planning for Natural Gas Distribution Martin Schmidt Networks Leibniz Universität Hannover We present a procedure for topology planning of large-scale Institute of Applied Mathematics real-world natural gas distribution networks. For a given [email protected] budget, it decides which combination of network extensions such as additional pipelines, compressors or valves should Marc Steinbach be added to increase the network’s capacity or enhance Leibniz Universität Hannover its operational flexibility. We formulate this as a nonlin- [email protected] ear mixed-integer problem. For its solution we use a combination of linear outer approximation and NLP solution Bernhard Willert techniques. Computational results obtained by a special Institute of Applied Mathematics tailored version of the MINLP solver SCIP are presented. Leibniz Universität Hannover [email protected] Armin Fügenschuh Zuse Institut Berlin [email protected] CP6 Technical Capacities of Gas Networks Thorsten Koch Zuse Institute Berlin Announcing the maximal technical capacities of gas net- [email protected] works is a legal demand against network operators. Exam- ining the gas network with detailed modeling of gas physics Jesco Humpola, Robert Schwarz, Thomas Lehmann, leads to highly nonlinear problems with discrete decisions. Jonas Schweiger, Benjamin Hiller, Jacint Szabo Occurring non-convexities and holes in the feasible region Zuse Insitut Berlin additionally complicate the computation of the maximal [email protected], [email protected], [email protected], technical capacity. With the help of minimal network ex- [email protected], [email protected], [email protected] amples the catch of the problem is explained and its complexity is shown.

CP6 Martin Schmidt Leibniz Universität Hannover Mixed-Integer-Programming Methods for Gas Institute of Applied Mathematics Network Optimization [email protected] We present methods to formulate and solve MINLPs originating in stationary gas network optimization. To this aim Marc Steinbach we use a hierachy of MIP-relaxations and a graph decom- Leibniz Universität Hannover position approach. Thus, we are able to give tight relax- [email protected] ations of the underlying MINLP. The methods we present can be generalized to other non-linear weakly-coupled net- Bernhard Willert work optimization problems with binary decisions. We give Institute of Applied Mathematics computational results for a number of real world instances. Leibniz Universität Hannover [email protected]

Lars Schewe, Bjoern Geissler Friedrich-Alexander-Universität Erlangen Nürnberg, CP6 Department Mathematik, EDOM Designing Multiple Energy Carrier Networks [email protected], [email protected] We consider a network design problem where single energy carrier networks are coupled by cogeneration plants. Mod- Alexander Martin eling the physical properties results in a complex mixed- University of Erlangen-Nürnberg integer nonlinear problem which is approximated by a [email protected] mixed-integer linear model using piecewise linear functions. This mixed-integer program is solved using a branch-and- Antonio Morsi cut approach which is enhanced by problem-specific mixed- Friedrich-Alexander-Universität Erlangen Nürnberg, integer programming methods. Department Mathematik, EDOM Andrea Zelmer, Debora Mahlke [email protected] Friedrich-Alexander-Universität Erlangen-Nürnberg 78 OP11 Abstracts

Lehrstuhl für Wirtschaftsmathematik illustrations for some probability density functions. [email protected], [email protected] Mariya Naumova Rutgers University, NJ, USA Alexander Martin [email protected] University of Erlangen-Nürnberg [email protected] András Prékopa Rutgers University [email protected] CP7 Finding Low-Rank Submatrices with Nuclear CP7 Norm and l1-Norm On Rate of Convergence of Discretization Methods We propose a convex optimization formulation using nu- for Semi-Infinite Minimax Problems clear norm and l1-norm to find a large low-rank submatrix for a given matrix. We are able to characterize the low- This presentation deals with semi-infinite minimax prob- rank and sparsity structure of the resulting solutions. We lems and their solution by discretization algorithms. These show that our model can recover low-rank submatrices for algorithms apply an algorithm map to solve approximate matrices with subgaussian random noises. We solve the problems obtained by replacing the uncountable number proposed model using a proximal point algorithm and ap- of functions in the original problem by a finite number of ply it to an application in image feature extraction. functions. We develop rate of convergence results for such algorithms as a computational budget increases and find Xuan Vinh Doan that the asymptotic rate is the same for different algorithm C&O Department maps used to solve the approximate problems. University of Waterloo [email protected] Johannes O. Royset Asst. Prof. Stephen A. Vavasis Naval Postgraduate School University of Waterloo [email protected] Dept of Combinatorics & Optimization [email protected] Eng Yau Pee Naval Postgraduate School Kim-Chuan Toh [email protected] National University of Singapore Department of Mathematics and Singapore-MIT Alliance CP7 [email protected] On Implementing a Homogeneous Interior-Point Algorithm for Nonsymmetric Conic Optimization CP7 Based on earlier work by Nesterov, an implementation of Convergence Properties for a Self-Dual Regulariza- a homogeneous interior point algorithm for nonsymmet- tion for Convex and Saddle Functions ric conic optimization is presented. The method computes The convergence properties for a one-parameter regulariza- (nearly) primal-dual symmetric approximate tangent dition technique for convex optimization problems are stud- rections followed by a primal centering procedure. Quasi- ied. Such regularization scheme, introduced by Goebel, Newton updating is employed to compute higher order di- has as its main feature its self-duality with respect to the rections and to reduce work in the centering process. Ex- usual convex (and saddle) conjugation. In particular, we tensive and promising computational results are presented show that if a saddle function has at least one saddle point, for facility location problems, entropy problems and ge- then the sequence of saddle points of the regularized saddle ometric programs; all formulated as nonsymmetric conic functions converges to the saddle point of minimal norm of optimization problems. the original one. Anders Skajaa, John Bagterp Jørgensen Alvaro J. Guevara Technical University of Denmark Louisiana State University [email protected], [email protected] Department of Mathematics [email protected] Per Christian Hansen Technical University of Denmark Informatics and Mathematical Modelling CP7 [email protected] Integration of Univariate and Bivariate Piecewise Higher Order Convex Functions by Bounding CP8 A new numerical integration method is proposed for uni- Adjoint Subgradient-Propagation by Algorithmic variate piecewise higher order convex functions. The Differentiation method uses piecewise polynomial lower and upper bounds on the function, created in connection with suitable dual Optimization problems in engineering often have noncon- feasible bases in the univariate discrete moment problem vex objective and constraints and require global optimiza- and the integral of the function is approximated by tight tion algorithms. Deterministic global optimization algo- lower and upper bounds on them. We provide the exten- rithms based on branch-and-bound methods solve relax- tion of the method for the bivariate case and numerical ations of the original program. These are constructed by convex/concave under-/over-estimators of the func- OP11 Abstracts 79

tions involved. One of the alternative methods to con- selection becomes susceptible to premature convergence as struct these estimating functions are McCormick relax- problem size increases. ations [McCormick, Computability of global solutions to factorable nonconvex programs: Part I. Convex underesti- Noraini Mohd Razali mating problems, Mathematical Programming, 1976]. In Ms. General this technique results in nonsmooth estimators. [email protected] Hence to obtain derivative information, subgradients are needed. These can be calculated using Algorithmic Dif- ferentiation (AD) techniques as shown in [Mitsos et al, CP8 McCormick-Based Relaxations of Algorithms, SIAM Jour- Metamodel-Based Global Optimization Using Dy- nal on Optimization, 2009] and [Corbett et al, Compiler- namic Radial Basis Function Generated Subgradient Code for McCormick Relaxations, ACM Transactions on Mathematical Software, submitted]. To enhance the efficiency of modern engineering optimiza- In this talk we present a method for calculating subgra- tions involving computational-intensive models, metamod- dients by an adjoint method which makes the complexity els become more and more attractive. The main contri- of subgradient computation independent of the number of bution of this work is to explore a new dynamic meta- optimization parameters. Thus one bottleneck on the way model approach based on radial basis function, which im- to large-scale global optimization is eliminated. proves the approximate accuracy of metamodel in the region which designers are interested in, and makes optimiza- Markus Beckers tion converged to the global optimization with minimum German Research School for Simulation Sciences evaluations of expensive models. In several testing prob- LuFG Informatik 12: STCE lems, the efficiency of SRBF is demonstrated. [email protected] Lei Peng School of Areospace Engineering Uwe Naumann Beijing Institute of Technology RWTH Aachen University [email protected] Software and Tools for Computational Engineering [email protected] Li Liu, Teng Long School of Aerospace Engineering Viktor Mosenkis Beijing Institute of Technology LuFG Informatik 12: STCE [email protected], [email protected] RWTH Aachen University [email protected] CP8 Alexander Mitsos Midaco on Continuous and Mixed Integer Space Department of Mechanical Engineering Applications Massachusetts Institute of Technology [email protected] MIDACO is a novel software for global optimization of continuous, combinatorial and mixed integer problems. The software is based on a stochastic Gauss approximation al- CP8 gorithm (also known as Ant Colony Optimization)thatin- Particle Swarm Optimization in the Analysis of the corporates the Oracle Penalty Method to handle nonlin- Two Process Model of Sleep Regulation ear equality and inequality constraints. This contribution discusses the application of MIDACO on some challeng- The two process model of sleep regulation is widely used ing optimization problems arising from space applications. to understand the sleep-wake cycle in humans. Although This is the well known set of continuous GTOP benchmark the model is typically tuned to produce monophasic sleep problems published by the ESA/ACT and a mixed inte- with a duration in the neighborhood of 8 hours, it also ger multi stage optimal control application, representing a admits solutions with a much richer character. By careful multi gravity assist interplanetary space mission. Compar- choice of objective function, a global optimization scheme ing the performance with other approaches on the GTOP such as particle swarm optimization can lead to a number benchmark set, MIDACO obtains very good results and of different stable sleep-wake scenarios. even reveals new best known solutions in some cases. In case of the mixed integer interplanetary mission, MIDACO Cavendish Q. McKay, David Hickman, Max Kenngott is able to provide a first solution to this kind of complex Marietta College application. [email protected], [email protected], [email protected] Martin Schlueter School of Mathematics University of Birmingham (UK) CP8 [email protected] Increased Solution Quality for the Tsp with Ga Rank-Based Selection Method Matthias Gerdts This study examines the solution quality of some travelling University of Wuerzburg salesman problem (TSP) instances solved with two genetic Germany algorithm (GA) selection schemes; proportional roulette [email protected] wheel and rank-based roulette wheel. By using the same crossover and mutation operation, the results show that Jan Rueckmann rank-based selection outperformed proportional selection University of Birmingham in reaching minimum travelling distance within acceptable UK computation time. Results also reveal that proportional [email protected] 80 OP11 Abstracts

CP8 [email protected] Optimal Positioning of Microphones for Engine Noise Measurement CP9 With an ever increasing air traffic,the reduction of noise A Hybrid Optimization Algorithm for Solving pollution due to engines is a major issue for aircraft manu- Time Dependent Pde-Constrained Optimization facturers.The prediction of the acoustic sources inside the Problems nacelle is essential to master the acoustic radiation of the engine and design noise reduction solution. Moreover, test One approach to solving time dependent PDE problems on facilities have to be optimized in terms of microphones parallel machines is to divide the time into intervals and es- positioning and number. An inverse method allowing to timate (by solving the problem on a coarse mesh first) the rebuild acoustic sources from microphones measurement initial conditions. One can then iterate to make the solu- is presented. It is based on a 3D parallel Boundary Ele- tion across the intervals be smooth. We describe a method ments Method solving the acoustic waves equation in the that integrates such an approach with the additional re- frequency domain and using a transfer matrix formulation. quirement to optimize some objective. We illustrate the The inverse problem is solved by a least square minimiza- algorithm by applying it to the optimal control of a flap- tion approach. Finally, a heuristic based on local search on ping wing and using a modified version of the code PITA a discretized subspace of possible locations (hill climbing, (Parallel Implicit Time-integration Algorithm). tabu search) is presented to solve the problem of optimal microphones positioning. The purpose is to find the loca- Walter Murray tion and the minimum number of microphones that recon- Dept of Management Science and structs at best an a priori known source. Engineering, Stanford University [email protected] Vassili Srithammavanh,Régis Lebrun, Stéphane alestra EADS INNOVATION WORKS Youngsoo Choi [email protected], [email protected], Stanford University [email protected] [email protected]

CP9 CP9 Milano: A Matlab-Based Toolbox for Minlp Recent Advances in Solving Milp Problems with Sas In this talk, we present details of MILANO (Mixed-Integer Linear and Nonlinear Optimizer), a Matlab-based tool- We give an overview of SAS software to solve various types box for solving mixed-integer optimization problems. For of optimization problems with a focus on mixed integer MINLP, it includes implementations of branch-and-bound linear programming. The talk discusses current research and outer approximation algorithms and solves the non- topics of the SAS/OR development team including search linear subproblems using an interior-point penalty method strategies, heuristics and LP integration. introduced by Benson and Shanno (2005) for warmstarts. Special consideration is given for problems with cone con- Philipp M. Christophel straints. Numerical results will be presented. SAS Institute Inc. [email protected] Hande Y. Benson Drexel University Department of Decision Sciences CP9 [email protected] Structure-Exploiting Parallel Solver for Tree- Sparse KKT Systems CP9 By exploiting the rich hierarchical structure in KKT sys- A New (Parallel) Algorithm for Nonlinear Pro- tems of tree-sparse programs recursive algorithms not only gramming reduce the solution computation to linear complexity but are also well suited for massive parallelization. A sophis- We propose a new parallel algorithm for solving the gen- ticated separation of the underlying tree structure reduces eral nonlinear constrained optimization problem on a set of communication and idle time and leads to an ideal exploita- shared-memory parallel processors. The algorithm is not a tion of the multicore system with an almost linear speed- direct parallelization of an existing method. The objective up. The parallel approach and computational results with in its design is to achieve an inherently parallel algorithm shared and distributed memory systems will be presented. that performs comparable to the state-of-the-art methods even when sequentially applied. The algorithm only re- Jens Hübner quires the solution of a sequence of unconstrained prob- Institute of Applied Mathematics lems and linear programs that are interrelated but can be Leibniz Universität Hannover solved concurrently to a degree. We provide numerical ex- [email protected] amples illustrating the potential of the proposed algorithm and study its convergence behavior. Marc Steinbach Leibniz Universität Hannover Figen Oztoprak [email protected] Sabanci Univeristy fi[email protected] CP10 Ilker S. Birbil Convergence Analysis of a Family of a Family of Sabanci University Damped Quasi-Newton Methods for Nonlinear Op- OP11 Abstracts 81

timization JoséMarioMart´ınez Department of Applied Mathematics In this talk we will extends the technique in the damped State University of Campinas BFGS method of Powell (Algorithms for nonlinear con- [email protected] straints that use Lagrange functions, Math. Program- ming, 14: 224–248, 1978), in augmented Lagrange and SQP methods for constrained ptimization, to a family of quasi- CP10 Newton methods with applications to unconstrained opti- Constrained Optimization Algorithms Using Direc- mization problems. An appropriate way for defining this tions of Negative Curvature damped-technique will be suggested to enforce safely the positive definiteness property for all quasi-Newton positive In this work, we show how to include low cost procedures to and indefinite updates. It will be shown that this technique improve directions of negative curvature within an interior- maintains the global and superlinear convergence property point algorithm for constrained optimization, extending re- of a restricted class of quasi-Newton methods for convex sults for the unconstrained case. The key feature is that functions. This property is also enforced on an interval of the directions are computed within the null subspace of nonconvergent quasi-Newton methods. Numerical experi- the Jacobian matrix of the constraints. Finally, some nu- ences will be described to show that the proposed technique merical experiments are presented, including real problems improves the performance of quasi-Newton methods sub- from the CUTEr collection, and simulated problems with stantially in certain robust cases (eg, the BFGS method) a controlled spectral structure. and significantly in inefficient cases (eg, the DFP method). Javier Cano,JavierM.Moguerza Mehiddin Al-Baali Rey Juan Carlos University Sultan Quaboos University [email protected], [email protected] [email protected] Francisco J. Prieto Carlos III University CP10 [email protected] On the Solution of the Gps Localization and Circle Fitting Problems CP10 We consider the problem of locating a user’s position from A Sparse Augmented Lagrangian Algorithm for a set of noisy pseudoranges to a group of satellites. Two dif- Minimizing the Kohn-Sham Energy ferent formulations are studied: the nonlinear least squares formulation in which the objective function is nonconvex With the constantly increasing power of computers, the and nonsmooth, and the nonlinear squared least squares realm of experimental chemistry is increasingly being variant in which the objective function is smooth, but brought in contact with the field of computational math- still nonconvex. We show that the squared least squares ematics. In particular, the ability to compute the charge problem can be solved efficiently, despite is nonconvexity. density, i.e., the probabilistic location of a molecule’s elec- Conditions for attainment of the optimal solutions of both trons, allows numerous properties of matter to be displayed problems are derived. The problem is shown to have tight graphically, as opposed to investigated in the chemistry lab. connections to the well known circle fitting and orthogonal As many current methods scale at a rate proportional to regression problems. Finally, a fixed point method for the the cube of the number of atoms, such problems are still nonlinear least squares problems is derived and analyzed. too large for direct ab initio computations. This work describes recent advances in using an augmented Lagrangian Amir Beck approach to minimizing a specific energy function under Faculty of Industrial Engineering and Management orthogonality-constraints. Scaling is obtained by relaxing TECHNION - Israel Institute of technology full-orthogonality and exploiting the local properties of the [email protected] molecular systems in question.

Dror Pan Marc Millstone Technion - Israel Institute of Technology Courant Institute of Mathematical Sciences [email protected] New York University [email protected]

CP10 Chao Yang A Globaly Convergent Inexact Restoration Method Lawrence Berkeley National Lab Using Lagrange Multipliers [email protected] In this work we present a new Inexact Restoration method, combining the basic ideas of the Fischer-Friedlander Michael L. Overton method with the use of Lagrange multipliers, a sharp La- New York University grangian as a merit function, and the use of a quadratic Courant Instit. of Math. Sci. model in the optimization fase. We show an example in [email protected] which the original method suﬀers from the Maratos eﬀect but not ours. Also a watchdog strategy combining this Juan C. Meza new global method with the Birgin-Mart´ınez local method Lawrence Berkeley National Laboratory is proposed. [email protected]

Luis Felipe Bueno Unicamp CP10 [email protected] Can Directional Hessian Reﬁnement Reduces 82 OP11 Abstracts

Quasi-Newton Iterations by More Than Half? Matthias Köppe Dept. of Mathematics Directional Hessian refinement was recently proposed for University of California, Davis, USA BFGS quasi-Newton method with BFGS as the refiner, ap- [email protected] proximately halving iteration numbers but doubling cost in each iteration. Here we report experiments in which DFP is Robert Weismantel used as the refiner for the DFP quasi-Newton method. Ex- ETH Zuerich perimental data showed that the DFP refiner consistently [email protected] reduces iteration numbers substantially for problems for which the DFP method converges slowly, and in one case it reduced iterations from 3975 to 73. CP11 Yu Zhuang Irreducible Infeasible Sets in Convex Integer Pro- Texas Tech University grams [email protected] In this paper we address the problem of the infeasibility of systems defined by convex inequality constraints, where CP11 some or all of the variables are integer. In particular, we provide an algorithm that identifies a set of all con- Lll-Based Polynomial Time Algorithm for Integer straints that may affect a feasibility status of the system Knapsacks after some perturbation of the right-hand sides. Further- In this talk we will discuss a recent application of lattice ba- more, we analyse properties of the irreducible infeasible sis reduction to the computational integer knapsack prob- sets and we investigate the problem of the maximal con- lem. We obtain a LLL-based polynomial time algorithm sistent partition, showing that for the considered class of that solves the problem subject to a geometric constraint. convex functions the system can be partitioned into two subsystems each of which has an integer solution.

Iskander Aliev Wieslawa T. Obuchowska Cardiﬀ University Department of Mathematics [email protected] Chowan College [email protected]

CP11 CP11 Cutting Planes for Mixed Integer Programs with Quadratic Constraints and Objectives Designing An Eﬃcient Branch-and-Bound Ap- proach for Exact Mixed-Integer Programming We discuss some heuristics to generate cutting planes for mixed-integer programs which have quadratic constraints We present a hybrid symbolic-numeric approach for solving or a quadratic objective, and present computational results mixed-integer-programming problems exactly over the ra- on a a number of instances, including some from Mittel- tional numbers. By performing many operations using fast mann’s library of instances. ﬂoating-point arithmetic and then verifying and correcting results using symbolic computation, exact solutions can Sanjeeb Dash be found without relying entirely on rational arithmetic. IBM T.J. Watson Research Center Computational results will be presented based on an ex- [email protected] act branch-and-bound algorithm implemented within the constraint integer programming framework SCIP.

Marcos Goycoolea Daniel Steﬀy Universidad Adolfo Ibanez, Chile GeorgiaTech [email protected] desteﬀ[email protected]

CP11 William Cook A Polynomial-time Algorithm for Separable Con- Georgia Institute of Technology vex Minimization over N-fold 4-block Decompos- [email protected] able IPs Thorsten Koch, Kati Wolter In this talk, we generalize N-fold IPs and two-stage Zuse Institute Berlin stochastics IPs with N scenarios to N-fold 4-block decom- [email protected], [email protected] posable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time solvable for any separable convex function that is to be CP12 minimized. This implies, for example, that for given fixed An Optimal Control of Probability Density Func- network, stochastic integer multi-commodity flow problems tions of Stochastic Processes with the Fokker- can be solved in polynomial time in the number of scenar- Planck Formulation ios and commodities and in the binary encoding length of the input data. An optimal control strategy of stochastic processes is formulated by using the Fokker-Planck model. The control Raymond Hemmecke objectives are defined based on the probability density Dept. of Mathematics functions and the optimal control is achieved as the min- Technische Univ. Munchen Germany imizer of the objective under the constraint given by the [email protected] Fokker-Planck equation. The purpose of the control is attaining a final target configuration, or tracking a desired OP11 Abstracts 83

trajectory, for which a receding-horizon algorithm over a plexity (POD, RANS, LES). Numerical results including sequence of time windows is implemented. unsteady problems and shape optimization will be given.

Mario Annunziato Rolf Roth Università degli Studi di Salerno TU Darmstadt Dipartimento di Matematica e Informatica [email protected] [email protected] Stefan Ulbrich Technische Universitaet Darmstadt CP12 Fachbereich Mathematik Optimal Flow Control Based on POD for the Can- [email protected] cellation of Tollmien-Schlichting Waves by Plasma Actuators CP12 We present a Model Predictive Control approach for the Optimal Control of a Melt Flow in Laser Cutting cancellation of Tollmien-Schlichting waves in the boundary layer. To control the flow a bodyforce is induced We consider optimal control for a mathematical model of a by a plasma actuator. Proper Orthogonal Decomposition melt flow in laser cutting. The optimization goal is to find a is used for the low-order description of the flow model. laser intensity function that keeps the two free boundaries We show methods for improving the reduced model whose of the flow region as close as possible to the stationary quality is verified in comparison to the results of a Finite solution. The dynamical behavior of the free boundaries Volume based Large Eddy simulation. Numerical results is described by a system of two nonlinear coupled partial of the cancellation will be presented. differential equations. We discuss theoretical aspects and propose a numerical solution. Jane Elsemüller Technische Universität Darmstadt Georg Vossen Graduate School of Computational Engineering Nonlinear Dynamics of Laser Processing (NLD) [email protected] RWTH Aachen University [email protected] Stefan Ulbrich Technische Universitaet Darmstadt Fachbereich Mathematik CP13 [email protected] Shortest Path Estimation of Mra Images Using Ge- netic Algorithm

CP12 MRA, a technique used to detect vascular pathologies dur- Crank-Nicolson and Störmer-Verlet Discretiza- ing brain surgery, provides 3D data of cerebral vascular tion Schemes for Optimal Control Problems with structures. Where it is difficult to access the region of Parabolic Partial Differential Equations interest, the best point of entry is found. Choosing the shortest path with the minimum inconvenience is a rout- In this talk we present a family of second order discretiza- ing problem. We discuss the use of Genetic Algorithm to tion schemes for parabolic optimal control problems based estimate the shortest path between two points in the sys- on Crank-Nicolson schemes with different time discretiza- tem of blood vessels in the brain using skeletonized MRA tions for state and adjoint state so that discretization and images. optimization commute. One of the schemes can be explained as the Störmer-Verlet scheme. So we can interpret Anthony Y. Aidoo the method in the context of geometric numerical integra- Eastern Connecticut State University tion. The Hamiltonian structure of parabolic optimal con- [email protected] trol problem is also discussed. Joseph Ackora-Prah Thomas Flaig Kwame Nkrumah University of Science and Technolygy Universität der Bundeswehr München Kumasi, Ghana Institut für Mathematik und Bauinformatik [email protected] thomas.fl[email protected]

Thomas Apel CP13 Universität der Bundeswehr München Influenza Vaccination Strategies When Supply Is [email protected] Limited

The aim of this work is to find alternatives that mitigate CP12 the transmission of influenza via limited vaccination in a Multilevel Optimization for Flow Control with Dis- finite (200 days) time period. To understand the dynamics crete Adjoints of transmission we will use an extension of the SIR model with data from the 1918-19 Pandemic Influenza. We use We present a technique to efficiently obtain the discrete ad- optimal control techniques to explore these constraints and joint via a sparsity-exploiting forward mode of Automatic provide a more realistic approach that public health Policy Differentiation. This approach has been applied to a fast makers can work with when facing a Pandemic threat. CFD code including turbulence models. Using the adjoint, we can apply multilevel optimization techniques. These Romarie Morales are well suited for flow control problems, since we have dif- Arizona State University ferent discretization levels and models of increasing com- [email protected] 84 OP11 Abstracts

Sunmi Lee policy and schedules purchases of gilts during a medium Mathematical, Computational and Modeling Sciences term planning horizon, based on weekly periods. In our Center, opinion, the stochastic programming framework provides Arizona State University, a ﬂexible and eﬀective decision support tool for planning [email protected] production of swine farm.

Carlos Castillo-Chavez Victor M. Albornoz Arizona State University and Univ Tech Fed Santa Maria Department of Mathematics Departamento de Industrias [email protected] [email protected]

Lluis M. Pl`a CP13 Departamento de Matem´atica. A Multiple Sequence Alignment Algorithm based Universidad de Lleida on Compression [email protected]

Multiple alignments play an important role in detecting SARA V. Rodr´ıguez-Sánchez conserved subregions among biological sequences and infer- Facultad de Ingeniera Mecánica y Eléctrica ring evolutionary history. Many alignment methods that Universidad Autónoma de Nuevo León. exist to date do not use the specific properties of biological sara@yalma.fime.uanl.mx sequences and suffer from bad quality or high computational cost. Here, we introduce an approach that is based on compression and combinatorial optimization techniques. CP14 It uses common subsequences to produce alignments and Optimization of Environmental Adaptation Poli- therefore runs faster on sets of sequences that share com- cies mon properties. Economic-environmental model with vintage capital is con- Susanne Pape structed to analyze the optimal balance among different FAU Uni-Erlangen, Germany categories of investments into the environmental adapta- Chair of EDOM tion that compensate negative consequences of environ- [email protected] mental hazards and changes. The model distinguishes three categories of adaptation measures that compensate Sebastian Pokutta the decrease of the environmental amenity value, compen- Massachusetts Institute of Technology sate the decrease of total productivity, and develop new [email protected] hazard-protected capital and technology. The results provide insight into rational environmental adaptation poli- Alexander Martin cies. University of Erlangen-Nürnberg [email protected] Natali Hritonenko Prairie View A&M University [email protected] CP13 Parameters Optimization in S-System Models us- Yuri Yatsenko ing Population-based Reverse Engineering Meth- Houston Baptist University ods [email protected] Reverse Engineering can be considered as a process from which is possible inferring structural and dynamics features CP14 of a given system from external observations and relevant Hydrocarbon Reservoir Production Optimization knowledge. RE techniques play a central role in systems under Uncertainty - A Case Example biology, since it is not only important a knowledge of genes and proteins, but also to understand their structures and Sequential Bayesian inversion methods are entering the do- dynamics. RE works for inferring genetic networks are main of updating the knowledge one has about physical based on evolutionary algorithms, because they are appli- properties of a reservoir from production measurements. cable where mathematical analysis fail. One example of these methods is the ensemble Kalman filter. The result of such methods is an ensemble of models Mario Pavone representing the posterior uncertainty. The task is to ap- Dept. of Maths and C.S. - University of Catania ply production optimization methods to the ensemble. We [email protected] present an evolutionary algorithm-based approach to that problem and apply it to a fairly large benchmark case. CP14 Oliver Pajonk A Multistage Stochastic Optimization Model for Institute of Scientific Computing Livestock Production Technische Universität Braunschweig [email protected] In this work the authors presents a stochastic optimization model for planning piglet production as a decision support Ralf Schulze-Riegert tool in the first stage of the pig supply chain. The model SPT Group GmbH includes the uncertainty in the sow biological behaviour as [email protected] well as in future prices, under a finite set of possible scenarios. The proposed model provides an optimal replacement OP11 Abstracts 85

Hermann G. Matthies Res. 18, 1993) presented an O(n2 min{n, C}) algorithm Institute of Scientiﬁc Computing to solve this problem and a linear program with MO(n3) Technische Universit¨at Braunschweig variables and inequalities, where n is the number of periods [email protected] and C the batch size. We provide a linear program of size O(n2 min{n, C}), that is, for C

Givenaweighteddirectedgraphwithaselectedrootnode CP14 and a set of terminal nodes, the directed Steiner tree prob- Piecewise Monotonic Regression Algorithm for lem (DSTP) is to find a directed tree of the minimal weight Problems Comprising Seasonal and Monotonic which is rooted in the root node and spanning all termi- Trends nal nodes. We consider the DSTP with a constraint on the total number of arcs (hops) in the tree. This prob- In this research piecewise monotonic models for problems lem is known to be NP-hard, and therefore, only heuristics comprising seasonal cycles and monotonic trends are con- can be applied in the case of its large-scale instances. For sidered. In contrast to the conventional piecewise mono- the hop-constrained DSTP, we propose local search strate- tonic regression algorithms, our approach can efficiently gies aimed at improving any heuristically produced initial exploit a priori information about temporal patterns. It Steiner tree. They are based on solving a sequence of hop- is based on reducing these problems to monotonic regres- constrained shortest path problems for which we have re- sion problems defined on partially ordered data sets. The cently developed efficient label correcting algorithms. The latter are large-scale convex quadratic programming prob- approach presented in this talk is applied to solving the lems. They are efficiently solved by the GPAV algorithm. problem of 3D placing unmanned aerial vehicles (UAVs) Amirhossein Sadoghi used for multi-target surveillance. The efficiency of our al- Department of Computer Science gorithms is illustrated by results of numerical experiments. Linköping University [email protected] Oleg Burdakov Linkoping University Oleg Burdakov [email protected] Linkoping University [email protected] Patrick Doherty Dept. of Computer and Information Science Anders Grimvall Linkoping University Department of Computer Science [email protected] Linköping University,Sweden [email protected] Kaj Holmberg Department of Mathematics CP14 Linkoping University [email protected] Smaller Compact Formulation for Lot-Sizing with Constant Batches Jonas Kvarnström, Per-Magnus Olsson We consider a variant of the classical lot-sizing problem in Dept. of Computer and Information Science which the capacity in each period is an integer multiple of Linkoping University some basic batch size. Pochet and Wolsey (Math. Oper. [email protected], [email protected] 86 OP11 Abstracts

CP15 the elements of the adjacency matrix of graph is such a Graph Products for Faster Separation of Wheel In- function whose global minimizer is a Hamiltonian cycle. equalities Finding the global minimizer is not without issues most of which are caused by symmetry induced from the existence A stable set in a graph G is a set of pairwise nonadjacent of multiple Hamiltonian cycles. We show that the use of vertices. The problem of finding a maximum weight sta- directions of negative curvature is instrumental is breaking ble set is one of the most basic NP-hard problems. An this symmetry. important approach to this problem is to formulate it as the problem of optimizing a linear function over the convex Walter Murray hull STAB(G) of incidence vectors of stable sets. Then one Dept of Management Science and has to solve separation problems over it. Cheng and Cun- Engineering, Stanford University ningham (1997) introduced the wheel inequalities and pre- [email protected] sented an algorithm for their separation using time O(n4) for a graph with n vertices and m edges. We present a new Jerzy Filar separation algorithm running in O(mn2 + n3 log n). CIAM University of South Australia Sven De Vries jerzy.fi[email protected] Universität Trier [email protected] Michael Haythorpe University of South Australia CP15 [email protected] Optimization Methods for Radio Resource Man- agement CP16 We consider heuristic methods for wireless telecommunica- First-Order Methods for Convex Optimization tions cellular systems in which each base station manages with Inexact Oracle the orthogonal radio resources for its own users. Inter-cell We introduce a new definition of inexact oracle for con- interference is an issue if nearby cells simultaneously use vex optimization problems, and study the first-order meth- the same resource. We discuss the fairness issue for users in ods (classical and fast gradients) based on this oracle. We the system. We have previously shown that our optimiza- link oracle accuracy and achievable solution accuracy, and tion problem is NP-hard and even inapproximable, unless show that only fast gradient suffers from error accumu- PisequaltoNP. lation, casting a doubt over its absolute superiority over Mikael P. Fallgren the classical gradient. We present applications to saddle- point problems and obtain a universal optimal method for Royal Institute of Technology (KTH) smooth and non-smooth convex problems. Optimization and Systems Theory [email protected] Olivier Devolder Center for Operations Research and Econometrics Université catholique de Louvain CP15 [email protected] A Continuous Quadratic Programming Formula- tion of the Vertex Separator Problem Fran¸cois Glineur A vertex separator of a connected graph G is a subset of Center for Operations Research and Econometrics vertices A whose removal splits G into two disconnected Universit subsets B and C. The Vertex Separator Problem is the ’e catholique de Louvain problem of finding the smallest such subset A when B and [email protected] C are subject to size constraints. We formulate the VSP as a continuous quadratic program and provide necessary Yurii Nesterov and sufficient conditions for local optimality which depend CORE only on the edges in the graph. Universite catholique de Louvain [email protected] James T. Hungerford University of Florida Department of Mathematics CP16 freerad@ufl.edu Bandgap Optimization of Photonic Crystals Via Semidefinite Programming and Subspace Methods William Hager University of Florida The mathematical formulation of bandgap optimization hager@ufl.edu problems is made tractable by discretizing and using the finite element method, yielding a series of finite-dimensional eigenvalue optimization problems that are large-scale and CP15 non-convex, with low regularity and non-differentiable ob- Algorithms for Computing a Hamiltonian Cycle by jective. By restricting to appropriate eigen-subspaces, Minimizing a Smooth Function we reduce the problem to a sequence of small-scale convex semidefinite programs (SDPs) for which modern SDP The holy grail of solving hard binary optimization prob- solvers can be efficiently applied. Among several illustra- lems is to find a smooth function whose minimizer are all tions we show that it is possible to achieve optimized pho- binary. We discuss algorithms based on a result that shows tonic crystals which exhibit multiple absolute bandgaps, minimizing a determinant of a matrix whose variables are whose structures show complicated patterns which are far OP11 Abstracts 87

diﬀerent from existing photonic crystals. [email protected]

Robert M. Freund Xiaoqi Yang MIT The Hong Kong Polytechnic University Sloan School of Management [email protected] [email protected]

H. Men CP16 National University of Singapore Implementation and Tests of An Optimal Algo- [email protected] rithm for Minimizing Convex Functions on Simple Sets JOEL Saa-Seoane M.I.T. We summarize an algorithm described by the authors for [email protected] minimizing continuously differentiable functions on simple sets, and incorporate to it adaptive procedures for using Cuong Nguyen, Pablo A. Parrilo, Jaime Peraire strong convexity constants. Then we show computational Massachusetts Institute of Technology results comparing our method to optimal algorithms by [email protected], [email protected], [email protected] Nesterov and by Auslender and Teboulle, and to other efficient methods for optimization on simple sets. Elizabeth W. Karas CP16 Federal Univ. of Paraná, Brazil Dep. of Mathematics An Optimal Algorithm for Minimizing Convex [email protected] Functions on Simple Sets

We describe an algorithm based on Nesterov’s and on Clovis C. Gonzaga Auslender and Teboulle’s ideas for minimizing a convex Federal Univ of Sta Catarina Lipschitz continuously differentiable function on a simple [email protected] convex set (a set into which it is easy to project a vector). The algorithm does not depend on the knowledge of Diane Rossetto any Lipschitz constant, and√ it achieves a precision for the University of Sao Paulo, Brazil objective function in O(1/ ) iterations. We describe the [email protected] algorithm and the main complexity result. Clovis C. Gonzaga CP16 Federal Univ of Sta Catarina Conjugate Gradient with Subspace Optimization [email protected] In this talk, we present Conjugate Gradient with Subspace Elizabeth W. Karas Optimization (CGSO), an algorithm for solving uncon- Federal Univ. of Paraná, Brazil strained optimization problems. CGSO is closely related Dep. of Mathematics to Nonlinear Conjugate Gradient and Nemirovsky-Yudin’s [email protected] algorithm from early 80’s, with advantages from each. We will address issues on implementation of the algorithm as Diane Rossetto well as its properties and convergence rate. In addition to its efficiency in practice, CGSO has a convergence rate of University of Sao Paulo, Brazil 1 [email protected] O(log ) for the class of strictly convex problems. Sahar Karimi CP16 University of Waterloo [email protected] Subgradient Methods for Convex Problem Based on Gradient Sampling Stephen A. Vavasis We present a new subgradient algorithm, based on gradient University of Waterloo sampling, to solve a nondifferentiable constrained convex Dept of Combinatorics & Optimization optimization problem. Our motivation comes from the fact [email protected] that the gradient is cheap to compute compared with the subgradient in many applications. We prove the convergence of our proposed algorithm for the primal problem. CP17 We also apply our algorithm to the Lagrangian dual of GloptLab - A Configurable Framework for Global a convex constrained optimization problem. Numerical re- Optimization and Introducing the Test Environ- sults demonstrate that our algorithms are comparable with ment some existing subgradient algorithms. GloptLab is an easy-to-use testing and development plat- Yaohua Hu form for solving quadratic optimization problems by using The Hong Kong Polytechnic University branch and prune and filtering. In order to avoid a loss [email protected] of feasible points, rigorous error estimation using interval arithmetic and directed rounding are used. Various new Chee Khian Sim and state-of-the-art algorithms implemented in GloptLab Department of Applied Mathematics are used to reduce the search space: constraint propaga- The Hong Kong Polytechnic University tion, linear relaxations, strictly convex enclosures, conic methods, probing and branch and bound. Other tech- 88 OP11 Abstracts

niques, such as finding and verifying feasible points, enable Faculty of Mathematics to find the global minimum of the objective function. The University of Vienna Test Environment is a free interface to efficiently test differ- [email protected] ent optimization solvers. It is designed as a tool for both developers of solver software and practitioners who just Hermann Schichl look for the best solver for their specific problem class. It University of Vienna enables users to choose and compare diverse solver rou- Faculty of Mathematics tines, organize and solve large test problem sets, select [email protected] interactively subsets of test problem sets, perform a statistical analysis of the results and automatically produce a LaTeX and PDF output. CP17 Surrogate Model Choice and Averaging Based on Ferenc Domes Dempster-Shafer Theory for Global Optimization Faculty of Mathematics, University of Vienna, Problems [email protected] The literature on solving global optimization problems us- Arnold Neumaier ing surrogate models shows that the surrogate model choice University of Vienna may greatly influence the solution quality. However, model Department of Mathematics uncertainty has thus far rarely been taken into account [email protected] when deciding for a specific model. This talk therefore focuses on Dempster-Shafer theory for combining and select- Martin Fuchs ing surrogate models during the optimization process. Ad- CERFACS vantages and disadvantages of this approach will be demon- Parallel Algorithms Team strated on numerical experiments. This is a collaborative [email protected] work between Tampere University of Technology and Cor- nell University. Hermann Schichl Juliane Mueller University of Vienna Tampere University of Technology Faculty of Mathematics Visiting Researcher at Cornell University [email protected] juliane.mueller@tut.fi

CP17 Christine A. Shoemaker A Multi-Step Interior Point Warm-Start Approach Cornell University for Stochastic Programming [email protected]

We present an Interior Point based multi-step solution ap- Robert Piché proach for stochastic programming problems, given by a Tampere University of Technology sequence of scenario trees of increasing sizes. These trees robert.piche@tut.fi can be seen as successively more accurate discretization of an underlying continuous probability distribution. Each problems in the sequence is warmstarted from the previ- CP17 ous one. We analyse the resulting algorithm, argue that it Exclusion Regions for Global Optimization Prob- yields improved complexity over either the coldstart or a lems naive two-step scheme, and give numerical results. Interval methods for GO often have the difficulty that sub- Andreas Grothey boxes containing no solution cannot be easily eliminated School of Mathematics if there is a nearby optimizer outside the box. Thus, near University of Edinburgh each solution, many small boxes are created by repeated [email protected] splitting. We discuss how to reduce this so-called cluster effect by defining exclusion regions around each opti- Marco Colombo mizer found, that are guaranteed to contain no other solu- University of Edinburgh tion. The proposed methods are implemented in the CO- m.colombo@ed,ac,uk CONUT Environment for global optimization. Hermann Schichl CP17 University of Vienna A Bound Constrained Interval Global Optimiza- Faculty of Mathematics tion Solver in the COCONUT Environment [email protected]

In this presentation we introduce coco gop ex, a general Mihaly Csaba Markot purpose interval branch–and–bound solver for bound con- Faculty of Mathematics strained global optimization. It is written as a solver com- University of Vienna ponent of the COCONUT Environment, a modular open- [email protected] source software environment for global optimization. Af- ter running coco gop ex on over 150 standard bound constrained test problems, we concluded that is is competitive CP17 with current state–of–the–art GO solvers such as BARON An Optimal Design of Ball Bearings Using Evolu- and outperforms them in many cases. tionary Algorithms Mih´aly Csaba Mark´ot In the optimum design of ball bearings the long life is one OP11 Abstracts 89

of the most important criterions. For solving constrained rithms, including a scheme for iterative adjustment of the non-linear optimization formulations, an optimal design penalty parameter, is proposed and analyzed. Promising methodology has been proposed by two evolutionary algo- numerical results with an MPC variant (which ﬁts within rithms, namely the artiﬁcial bee colony and genetic algo- the framework) are reported. rithms. A sensitivity analysis of various design parameters, using the Monte Carlo simulation method, has been per- Andre L. Tits formed to see changes in the dynamic capacity. There is an University of Maryland, College Park excellent improvement found in optimized bearing designs. Dept of ECE and Institute for Systems Research [email protected]

Rajiv Tiwari Meiyun Y. He Professor, Department of Mechanical Engineering University of Maryland, College Park IIT Guwahati [email protected] [email protected]

U. Venkatesu CP18 Graduate Student, IIT Guwahati The Accuracy of Interior-Point Methods Based on [email protected] Kernel Functions Interior-point methods that use barrier functions induced CP18 by some real univariate kernel functions have been studied Solving Highly Symmetric Integer Linear Pro- for the last decade. In these IPM’s the algorithm stops grams when finds a solution such that is close enough (in the barrier function sense) to a point in the central path such that We present a new algorithm which solves integer linear satisfies some accuracy conditions. But this does not di- programs of dimension n with symmetry groups isomorphic rectly imply that we got a solution that has the desired to the alternating or the symmetric group of order n.The accuracy. In this talk, we analyze the accuracy of the so- main idea of the algorithm is to reduce the problem to a lution produced by the mentioned algorithm. feasibility check of a linear number of certain points lying close to the fixed space of the symmetry group. This is Manuel Vieira joint work with Richard Bödi and Michael Joswig. Delft University of Technology [email protected] Katrin Herr TU Darmstadt [email protected] CP18 Strange Behaviors of Interior-Point Methods for Solving Semidefinite Programming Problems in CP18 Polynomial Optimization A Bound for the Number of Different Basic Solu- tions Generated by the Simplex Method We observe that in a simple one-dimensional polynomial optimization problem (POP), the ’optimal’ values of In this presentation, we give an upper bound for the num- semidefinite programming (SDP) relaxation problems re- ber of different basic feasible solutions generated by the ported by the standard SDP solvers converge to the op- simplex method for linear programming problems having timal value of the POP, while the true optimal values of optimal solutions. The bound is polynomial of the num- SDP relaxation problems are strictly and significantly less ber of constraints, the number of variables, and the ratio than that value. Some pieces of circumstantial evidences between the minimum and the maximum values of all the for the strange behaviours of the SDP solvers are given. positive elements of primal basic feasible solutions. When This result gives a warning to users of the SDP relaxation the primal problem is nondegenerate, it becomes a bound method for POPs to be careful in believing the results of for the number of iterations. We show some basic results the SDP solvers. We also demonstrate how SDPA-GMP, when it is applied to special linear programming problems. a multiple precision SDP solver developed by one of the The results include strongly polynomiality of the simplex authors, can deal with this situation correctly. method for Markov Decision Problem by Ye and utilize its analysis. Hayato Waki The University of Electro-Communications Tomonari Kitahara, Shinji Mizuno [email protected] Tokyo Institute of Technology [email protected], [email protected] Maho Nakata RIKEN [email protected] CP18 Infeasible Constraint-Reduced Interior-Point for Masakazu Muramatsu Linear Optimization University of Electro-Communications Constraint reduction in the context of interior-point meth- [email protected] ods can yield substantial computational savings per iteration for linear programs with many more inequality con- CP18 straints than variables in standard dual form. Previously proposed constraint-reduced algorithms require initial dual Symmetry in the Basis Partition of the Space of feasibility. Here an exact-penalty-based framework for in- Linear Programs feasible constraint-reduced primal-dual interior-point algo- A linear program (LP) is associated with an optimal basis. 90 OP11 Abstracts

The space of linear programs (SLP) can be partitioned into [email protected] a finite number of sets, each consisting of all LPs with a common basis. If the partition of SLP can be characterized, we can solve infinitely many LPs in closed form. A CP19 tool for characterizing the partition of SLP is a dynamical A Class of Preconditioners for Newton-Krylov system on the Grassmann manifold M’=h(M), where M is Methods in Large Scale Optimization a projection matrix. An LP defines a projection matrix, starting from which the solution of M’=h(M) converges to In this work, we propose a class of preconditioners for a limit projection matrix which can determine the basis of Newton-Krylov methods in nonconvex large scale uncon- the LP. Some properties on structures of the partition, in strained optimization. We focus on the solution of the particular, symmetric structures, will be presented. large scale (possibly indefinite) linear system which arises at each iteration of any truncated Newton method. In par- Gongyun Zhao ticular, we use the set of directions generated by Krylov Department of Mathematics subspace methods, as by product, to provide the precondi- National University of Singapore tioners. [email protected] Massimo Roma Dipartimento di Informatica e Sistemistica CP19 SAPIENZA - Universita’ di Roma Flash Crash, Market Impact, and Stability of Op- [email protected] timal Execution Strategy Giovanni Fasano The U.S. market Flash Crash on May 6, 2010 illustrated Dip. Matematica Applicata effect of trading impact and challenges in optimal execu- Universita’ Ca’ Foscari di Venezia tion. In this talk, I will describe market price and impact [email protected] models which have been proposed for developing optimal execution algorithms. In addition, I will present properties of the resulting execution algorithms, describe sensitivity of CP19 execution strategies to market impact functions, and how On Saddle Points in Nonconvex Semi-Infinite Pro- to achieve better stability using robust optimization and gramming regularized robust optimization. *This is joint work with T. F. Coleman and S. Moazeni We apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under Yuying Li the reduction approach it is shown that, locally around a School of Computer Science local minimizer, this problem can be transformed equiv- University of Waterloo alently in such a way that the transformed Lagrangian [email protected] fulfills saddle point optimality conditions. These results allow that local duality theory and corresponding numerical methods (e.g. dual search) can be applied to a broader CP19 class of nonconvex problems. Optimization with Time-Periodic PDE Con- straints: Numerical Methods and Applications Jan-J Ruckmann University of Birmingham Optimization problems with time-periodic parabolic PDE [email protected] constraints can arise in important chemical engineering applications, e.g., in periodic adsorption processes. We Francisco Guerra Vazquez present a novel direct numerical method for this problem University of the Americas class. The main numerical challenges are the high non- [email protected] linearity and high dimensionality of the discretized problem. The method is based on Direct Multiple Shooting and inexact Sequential Quadratic Programming with glob- Ralf Werner alization of convergence based on natural level functions. Hochschule Munich We highlight the use of a generalized Richardson iteration [email protected] with a novel two-grid Newton-Picard preconditioner for the solution of the quadratic subproblems. At the end of the CP19 talk we explain the principle of Simulated Moving Bed processes and conclude with numerical results for optimization Necessary Optimality Conditions for the O-D Ma- of such a process. trix Adjustment Problem

Andreas Potschka Most of the work on this topic has been based on assuming Interdisciplinary Center for Scientific Computing that the traffic assignment problem admits a unique opti- University of Heidelberg mal flow in a certain neighborhood, which is very strong. [email protected] Hence, designing necessary optimality conditions for the problem appears to be crucial, since it is typically nonsmooth. Only Fritz-John’s type necessary optimality con- Hans Georg Bock ditions have been derived so far. In this talk, we present IWR, University of Heidelberg some approaches to obtain Karush-Kuhn-Tucker type op- [email protected] timality conditions using mathematical tools from variational analysis. Johannes Schl˝oder Interdisciplinary Center for Scientific Computing Alain B. Zemkoho, Stephan Dempe University of Heidelberg Instiut of Numerical Mathematics and Optimization OP11 Abstracts 91

TU Bergakademie Freiberg [email protected] [email protected], [email protected] Andreas Adelmann Paul Scherrer Institut CP20 [email protected] Simulation of Interface Evolution for Several Phases Using a Primal-Dual Active Set Method Peter Arbenz Interface evolution with applications including material sci- ETH Zurich ence (e.g. grain growth), image processing and geology can Chair of Computational Science be modelled using a phase field approach. In particular, [email protected] we consider an Allen-Cahn variational inequality and include nonlocal constraints to guarantee mass conservation. Costas Bekas Moreover, due to the consideration of several phases, we IBM Research study a system of inequalities. Simulation in time leads to Zurich Research Laboratory a sequence of optimization problems, where the unknowns [email protected] are vector valued functions in space, which have to ly in the Gibbs-Simplex and additionally have to fulfill an integral Alessandro Curioni condition. We propose and analyze a primal-dual active IBM Research-Zurich set method for the solution. Convergence of the algorithm [email protected] is shown and numerical simulations in two and three dimensions as well as for two and more phases are presented demonstrating its efficiency. CP20 Sensitivity-Based Optimization of Navier-Stokes Luise Blank Problems with Heat Transfer NWF I - Mathematik Universität Regensburg This work presents the methodology of a sensitivity analy- [email protected] sis utilizing the continuous sensitivity equation approach regarding laminar, incompressible fluid flows with heat transfer. The arising set of equations is solved with an effi- CP20 cient finite-volume solver on a block structured grid. Fur- Wind Climatologies from a Mass-Consistent Wind thermore, the resulting sensitivities of the flow concerning Model for Small Terrain changes in boundary conditions such as velocities and temperature as well as geometric variations using NURBS are Wind measurements in Sri Lanka are sparse particularly presented via a generic testcase. in the hill country of Sri Lanka and interpolation of these observations provides unrealistic wind patterns in moun- Johannes Siegmann, Julian Michaelis, Michael Schaefer tainous areas. Here we use a mass-consistent wind model Fachgebiet Numerische Berechnungsverfahren that takes account of topography to compute monthly wind TU Darmstadt climatologies for Sri Lanka at a resolution of 6 km. The [email protected], [email protected] model predicts realistic wind fields and brings out the high darmstadt.de, [email protected] wind speed at various gaps in the mountain ridges in Sri Lanka. Quantitative comparison with measurements at stations across Sri Lanka shows that the predictions are CP20 reasonably realistic. Thus this technique provides detailed An Interior-Point Algorithm for Shakedown Anal- and useful wind climatologies that can be used for research, ysis of Large-Scale Engineering Structures development and applications purposes. An interior-point algorithm for the computation of shake- Ajith Gunaratne down loads of large-scale engineering structures subjected Florida A & M University to varying thermo-mechanical loading is presented. The Department of Mathematics according optimization problem is characterized by a large [email protected] number of variables and constraints. Thus, the calculation can be computationally expensive and time-consuming. A selective algorithm is introduced to overcome this prob- CP20 lem by dynamic reduction of the entire system to critical Multi-Objective PDE Constrained Optimization substructures. The method is illustrated by numerical ex- for a 250 MeV Injector amples in mechanical engineering.

We present a PDE constrained multi-objective optimiza- Jaan W. Simon, Dieter Weichert tion model for the 250 MeV electron injector to be com- Institute of General Mechanics missioned at Paul Scherrer Institut. Realizing good beam RWTH Aachen University quality (compact in phase space) and attaining the de- [email protected], [email protected] sign energy are crucial to achieve the desired performance. In this context, state of the art massively parallel multiobjective optimization algorithms will be instrumental for the optimal design of the injector. We discuss suitable CP20 multi-objective optimization algorithms and plans for their An Iterative Regularization Algorithm for Opti- implementation. mization in Parameters Identification Problems. Yves Ineichen In this work we present an iterative regularization algo- ETHZ rithm for solving a parameter identification problem rela- PSI tive to a system of diffusion, convection and reaction equa- 92 OP11 Abstracts

tions (state equations). The parameters to be identified are Algorithm the diffusivity and reaction terms. The problem is solved by means of a succession of nonlinear constrained opti- In this paper, we propose new stochastic gradient descent mization problems. The problems are ill-posed and need algorithms for solving convex composite optimization prob- regularization. For each problem, the proposed algorithm lems. Our algorithms utilize a stochastic approximation of computes the sequence of regularization parameters by us- the gradient of the smooth component of objective func- ing the lagrangian dual formulation of the constrained options in each iteration. We prove that the expectation timization problem. The state parameters are computed and the variance of the solution errors converge to zeros. by truncated iterative solution of the inner system. The The convergence rates are proved using the arguments of effectiveness of the method is evaluated on 1D and 2D test stochastic estimate sequences. When applied to regular- problems with different levels of noise in the measurements. ized regression problems, our algorithms distinguish from other stochastic gradient methods by preserving sparsity structures in the solutions in all iterations. Fabiana Zama Department of Mathematics, University of Bologna Qihang Lin [email protected] Carnegie Mellon University Tepper School of Business Elena Loli Piccolomini [email protected] Department of Mathematics, University of Bologna Xi Chen [email protected] Carnegie Mellon University School of Computer Science [email protected] CP21 Scenario Decomposition of Risk-Averse Multistage Javier Peña Stochastic Programming Problems Carnegie Mellon University Tepper School of Business For a risk-averse multistage stochastic optimization prob- [email protected] lem with a finite scenario tree, we introduce a new scenario decomposition method and we prove its convergence. The main idea of the method is to construct a family of risk- CP21 neutral approximations of the problem. The method is Efficient Bayesian Updating of Parameters for Heat applied to a risk-averse inventory and assembly problem. and Moisture Transport in Heterogenous Materials

Ricardo A. Collado The Bayes formula can be used to provide a reliable esti- IOMS-Operations Management Group mation of the probability distributions of heat and mois- Stern School of Business, NYU ture transport in structures. It combines a priori infor- [email protected] mation about material properties and measurment data. We present a new method to numericaly compute a Bayes Andrzej Ruszczynski update in a direct, fast and reliable manner. As an exam- Rutgers University ple we focus on the description of heterogeneous material MSIS Department which includes the uncertainty in material parameters to- [email protected] gether with its spatial ﬂuctuations.

David Papp Bojana V. Rosic Rutgers Center for Operations Research Institute of Scientiﬁc Computing [email protected] TU Braunschweig [email protected]

CP21 Hermann G. Matthies, Oliver Pajonk Uncertainty Modeling for Robust Optimization Institute of Scientific Computing Technische Universität Braunschweig Polyhedral clouds have recently demonstrated strength in [email protected], [email protected] dealing with higher dimensional uncertainties in robust optimization, even in case of partial ignorance of statistical ANNA Kucerova, JAN Sykora information. However, in real-life applications the compu- Faculty of Civil Engineering, Prague, Czech TU tational effort to account for robustness, i.e., to find worst- [email protected], [email protected] case scenarios, should not exceed certain limitations. We propose a simulation-based approach for optimization over a polyhedron, inspired by the Cauchy deviates method. CP21 Thus we achieve a tractable method to compute worst-case Bundle Methods for Hydro Reservoir Management scenarios with polyhedral clouds. with Joint Chance Constraints Martin Fuchs In the electrical industry, offer-demand equilibrium prob- CERFACS lems for hydrothermal systems are often solved by using Parallel Algorithms Team price decomposition techniques. In this setting, the partic- [email protected] ular sub-problems optimizing one hydraulic valley are typically large-scale combinatorial network flow problems. The combinatorial nature of such problems is due to complex CP21 dynamic constraints on the watershed controls. For these A Sparsity Preserving Stochastic Gradient Descent reasons, such problems are often considered in a determin- OP11 Abstracts 93

istic setting, even though reservoir streamflow is uncertain get in expanding the railway infrastructure to cope with in practice. We propose to tackle uncertainty (in a contin- future demands. Our model views the problem as a net- uous setting, without complex watershed constraints) by work design problem with an underlying routing problem. formulating the flow constraints using joint chance con- It considers a long-term planning horizon, where expensive straints. We consider inflows following any causal time measures can be stretched over several years. We also give series model with Gaussian innovations. The sub-problem computational results on real-world instances. is convex, with probabilistic constraints defined in a highly dimensional cube that can be efficiently evaluated by the Andreas Bärmann so-called Genz code. Since the cutting planes technique Friedrich-Alexander-Universität Erlangen-Nürnberg takes too many iterations to converge to an accurate solu- [email protected] tion rapidly, we consider how to use a constrained variant of the bundle method, capable of handling inaccurate sub- Alexander Martin gradient calculations. The approach is assessed on a real- University of Erlangen-Nürnberg size hydro-sub-problem typical of the French power mix. [email protected]

Sebastian Pokutta Wim Van Ackooij Massachusetts Institute of Technology EDF R&D [email protected] Department OSIRIS [email protected] CP22 Rene Henrion Optimization of Gas and Water Supply Networks Weierstrass Institute Berlin, Germany The optimal control of gas and water supply networks is a [email protected] challenging task. The dynamics in both types of networks are governed by hyperbolic systems of PDEs. Additionally, Claudia A. Sagastizabal components like compressor/pumping stations and valves IMPA introduce binary decisions in the optimal control problem. [email protected] A key ingredient is to efficiently solve the underlying simulation task with reliable error bounds. Therefor, we apply Riadh Zorgati adjoint-based error estimators. This approach also pro- EDF R&D vides gradient information for the optimization. Department OSIRIS Pia Domschke, Oliver Kolb [email protected] TU Darmstadt [email protected], CP21 [email protected] Approximate Dynamic Programming with Bezier Curve Approximations for Top Percentage Traffic Jens Lang Routing Department of Mathematics Darmstadt University of Technology This study investigates the optimal routing strategy under [email protected] multi-homing where cost are computed with top-percentile pricing. This problem is stochastic and large. Solution approaches based on Stochastic Dynamic Programming re- CP22 quire discretization in state space, which suffers from the Bounded Diameter Minimum Spanning Trees: A curse of dimensionality. To overcome this we use Approxi- New Approach Combining Branch-and-Bound and mate Dynamic Programming to construct approximations Enumeration Algorithms of value function, and develop Bezier Curves/Surfaces aggregation in time. This accelerates the efficiency of param- We address the problem of computing diameter- eter training, which makes the real-sized TpTRP tractable. constrained minimum spanning trees. So far this problem has mainly been investigated for the case of unit length. We aim at exploring the more general case where the length Xinan Yang of the edges can be any number. To approach this prob- University of Edinburgh lem, we develop a new algorithm combining branch-and- [email protected] bound procedures with enumeration algorithms for spanning trees. The latter can be used for producing upper and Andreas Grothey lower bounds. Computational experiments are reported. School of Mathematics Ute Guenther University of Edinburgh TU Darmstadt [email protected] FB Mathematics [email protected] CP22 Planning the Expansion of Railway Networks A Alexander Martin Network Design Problem University of Erlangen-Nürnberg [email protected] We present a mixed integer model to support the decision process at Deutsche Bahn, the largest European Railway Company, on how to optimally invest their annual bud- CP22 A Polyhedral Approach for Solving Two-Facility 94 OP11 Abstracts

Network Design Problem when solving the evolution equations. Implicit in the Ein- stein constraint equations is an additional simple inequal- The paper studies the problem of designing telecommu- ity. We look at solving these equations using barrier meth- nication networks using transmission facilities of two dif- ods together with a traditional finite element approach. ferent capacities. We fully characterize and enumerate all the extreme points of the 3-node subproblem polyhedron. Jennifer Erway A new approach for computing facets is introduced and a Wake Forest University new family of facets is identified. The 3-partition based [email protected] facets strengthen the linear programming formulation to a great extent. Computational results show these facets significantly reduce integrality gap and size of the branch- CP23 and-bound tree. Nonlinear Optimum Experimental Design for In- dustrial Processes Faiz Hamid, Yogesh K. Agarwal Indian Institute of Management, Lucknow, India Dynamical processes from industry can be modeled by sys- [email protected], [email protected] tems of differential equations. These models have to be validated by estimation of unknown parameters from experimental data. Designing experiments which minimize CP22 the uncertainty of the parameters leads to intricate non- On Clearing Coupled Day-Ahead Electricity Mar- standard optimal control problems. This talk presents re- kets cent advances in the formulation and solution methods of these problems including adjoint differentiation, multiple The European power grid is divided into several market shooting and an online approach. Examples from the prac- areas connected by power lines with restricted transmission tice of our industrial partners are given. capacity. Hence supply and demand of adjacent areas can not always be balanced. The goal of a day-ahead auction is Stefan Körkel to determine prices and cross border flow maximizing the Interdisciplinary Center for Scientific Computing economic surplus of all participants. Also the transmission Heidelberg University and distribution losses must be considered. A MIQP is [email protected] used to model this challenge.

Johannes C. Müller, Alexander Martin CP23 University of Erlangen-Nürnberg Optimization under Uncertainty of a Wind Turbine [email protected], [email protected] In this work a model of wind turbine is presented, considering a variable pitch and rotational speed control, fluid- Sebastian Pokutta structural interaction and acoustics. Hence a typical tur- Massachusetts Institute of Technology bine design is analyzed under uncertainty (e.g. wind speed) [email protected] by the use of a Simplex Elements Stochastic Collocation (SESC) method, based on adaptive grid refinement of a simplex elements discretization in probability space. The CP23 approach is equally robust as Monte Carlo (MC) simulation Model Hierarchy Based Multilevel SQP-Methods in terms of the Extremum Diminishing (ED) robustness for PDAE-Constrained Optimal Control Problems concept. In conclusion a process of shape optimization un- with Application to Radiative Heat Transfer der uncertainty via genetic algorithms will be considered. We present a multilevel-SQP-method, applied to a radia- Giovanni Petrone, Carlo De Nicola tive heat transfer problem in glass manufacturing. To han- Università degli Studi di Napoli Federico II dle the direction- and frequency-dependent radiation, we [email protected], [email protected] make use of series expansion and discretize the continuous frequency spectrum into different bands. The focus is Domenico Quagliarella on the multilevel strategy, which is based on a hierarchy Centro Italiano Ricerche Aerospaziali of mathematical models and a sequence of adaptive space- [email protected] time discretizations with increasing accuracy. Mathemat- ical models are obtained by varying the expansion order Gianluca Iaccarino and the number of frequency bands. Stanford University [email protected] Debora Clever Graduate School CE, Technische Universität Darmstadt Jeroen Witteveen [email protected] Stanford University Center for Turbulence Research [email protected] CP23 Solving the Einstein Constraint Equations Using CP23 Barrier Methods Optimum Experimental Design for Advection- The Einstein field equations for general relativity describe Diffusion-Reaction Problems how gravity interacts with matter and energy. The equations are a system of ten coupled equations, comprised of Optimum Experimental Design is the task of finding an six evolution equations and four constraint equations. The experiment that behaves best in the sense of reducing un- constraint equations must be enforced at each time step certainties in the parameters that are to be estimated from OP11 Abstracts 95

it. With PDE constraints new challenges arise for this op- TU Darmstadt, Department of Mathematics timization problem. We want to present an adjoint mode Discrete Optimiation for the costly gradient calculation following Automatic Dif- [email protected] ferentiation principles and discuss questions for the placing of measurement points in time and space. Lars Schewe Friedrich-Alexander-Universität Erlangen Nürnberg, Andreas Schmidt Department Mathematik, EDOM Interdisciplinary Center For Scientific Computing, [email protected] Heidelberg [email protected] Jakob Schelbert Friedrich-Alexander-Universität Erlangen-Nürnberg CP24 Department Mathematik, EDOM Multilevel Shape Optimization for the Instationary [email protected] Navier-Stokes Equations Kai Habermehl We consider shape optimization problems governed by the TU Darmstadt, Department of Mathematics instationary incompressible Navier-Stokes equations. We Nonlinear Optimization use an approach based on transformations of a reference [email protected] domain which is very flexible and allows arbitrary types of parametrizations. Shape derivatives are derived in a continuous adjoint approach. Our focus is on the efficient CP24 numerical solution of discretized shape optimization prob- Nonlinear Elastic Shape Optimization and Uncer- lems. This is achieved by using multilevel optimization tain Loading with adaptivity based on goal oriented error estimators. Numerical results are presented. Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear Christian Brandenburg deformations and nonlinear hyperelastic constitutive laws. TU Darmstadt A weighted sum of the structure compliance, its weight, Germany and its surface area are minimized. The resulting nonlin- [email protected] ear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. In- Stefan Ulbrich deed, there exist different definitions for the compliance: Technische Universitaet Darmstadt the change in potential energy of the surface load, the Fachbereich Mathematik stored elastic deformation energy, and the dissipation as- [email protected] sociated with the deformation. Furthermore, elastically optimal deformations are no longer unique so that one has to choose the minimizing elastic deformation for which the CP24 cost functional should be minimized, and this complicates New Discrete Approach for Topology-Optimization the mathematical analysis. Additionally, along with the in Mechanical Engineering non-uniqueness, buckling instabilities can appear, and the compliance functional may jump as the global equilibrium The new discrete approach combines simple but very pow- deformation switches between different bluckling modes. erful ideas for topology optimizations. No gradient infor- This is associated with a possible non-existence of optimal mation is necessary to reduce and add material. Here a shapes in a worst-case scenario. controller-mechanism is used. Only the changes of target In this paper the sharp-interface description of shapes is function, e.g. displacements or reaction forces, are nec- relaxed via an Allen–Cahn or Modica–Mortola type phase- essary to solve the optimization problem. All non-linear field model, and soft material instead of void is considered effects in FEM-simulations can be considered. The sim- outside the actual elastic object. An existence result for ple and basic approach solves the optimization problems optimal shapes in the phase field as well as in the sharp- (academic examples as well as industrial problems) in an interface model is established, and the model behavior amazing way. for decreasing phase-field interface width is investigated in terms of Γ-convergence. Computational results are based Sierk Fiebig on a nested optimization with a trust-region method as the Volkswagen inner minimization for the equilibrium deformation and a sierk.fi[email protected] quasi-Newton method as the outer minimization of the actual objective functional. CP24 Martin Rumpf Actuator Positioning in Truss Topology Design Rheinische Friedrich-Wilhelms-Universität Bonn Institut für Numerische Simulation The aim is to find the optimal topology of a truss and [email protected] the optimal positioning of the actuators within this truss by solving just one optimization problem. The actuators Benedikt Wirth are modelled as binary variables so we get a MINLP. We Rheinische Friedrich-Wilhelms-Universität Bonn are going to compare different models, such as a semidef- [email protected] inite MIP, a MIP and a quadratic MIP. For solving the MISDP we put a branch-and-bound-framework together with a SDP-solver. First computational results are pre- Patrick Penzler sented. Universität Bonn [email protected] Sonja Friedrich 96 OP11 Abstracts

CP24 Yair Censor An Approximation Technique for Robust Shape University of Haifa Optimization Department of Mathematics [email protected] We present a second-order approximation for the robust counterpart of general nonlinear programs with state equa- Simeon Reich tion given by a PDE. We show how the approximated ro- Department of Mathematics, bust counterpart can be formulated as trust-region problem The Technion - Israel Institute of Technology which can be solved efficiently using adjoint techniques. [email protected] This method is applied to shape optimization in structural mechanics in order to obtain optimal solutions that are robust with respect to uncertainties in acting forces and CP25 other quantities. Numerical results are presented. Second-Order Cone Based Reformulation for Ro- bust Wardrop Equilibrium Problems Adrian Sichau TU Darmstadt, Department of Mathematics In this paper, we define the notion of robust Wardrop equi- Research Group Nonlinear Optimization librium for traffic model with uncertain data. Particularly, [email protected] we show that the problem of finding such an equilibrium can be cast as a second-order cone complementarity prob- Stefan Ulbrich lem, when the uncertain data are expressed by means of Technische Universitaet Darmstadt Euclidean norms. We also report some numerical results Fachbereich Mathematik to observe the behavior of obtained equilibria with various [email protected] choices of uncertainty structures. Yoshihiko Ito, Hitoshi Takahashi CP25 Kyoto University A Family of Dantzig-Wolfe Type Decomposition [email protected], [email protected] Algorithms for Variational Inequality Problems. Shunsuke Hayashi We present a family of algorithms for variational inequal- Dept of Applied Mathematics and Physics ities based on ideas of Dantzig-Wolfe decomposition for Graduate School of Informatics, Kyoto University linear programming. Constraints of the problem are sep- [email protected] arated into ”hard” and ”easy”. At each iteration, two subproblems are solved. One deals with easy constraints, dualizing hard using Lagrange multipliers provided by the CP25 second subproblem. Second subproblem involves hard con- Interior-Point Method for Nonlinear Programming straints, reducing variables restricting to convex hull of pre- with Complementarity Constraints viously generated points. Various approximations of the constraints and VI mapping are allowed. We propose an algorithm for solving nonlinear programming problems with complementarity constraints, which Juan Pablo Cajahuanca Luna is based on the interior-point approach. Main theoreti- Instituto de Matemática Pura e Aplicada IMPA cal results concern direction determination and step-length [email protected] selection. We use an exact penalty function to remove complementarity constraints. Thus a new indefinite linear Mikhail V. Solodov system is defined with a tridiagonal low-right submatrix. Inst de Math Pura e Applicada Furthermore, new merit function is defined, which includes [email protected] barrier, exact penalty, and augmented Lagrangian terms.

Claudia Sagastiz´abal Ladislav Luksan, Ctirad Matonoha,JanVlcek CEPEL Institute of Computer Science [email protected] Academy of Sciences of the Czech Republic [email protected], [email protected], [email protected]

CP25 CP25 The Split Variational Inequality Problem Two Strong Convergence Theorems for Bregman We propose a new variational problem which we call the Strongly Nonexpansive Split Variational Inequality Problem (SVIP). It entails finding a solution of one Variational Inequality Problem We study the convergence of two iterative algorithms (VIP), the image of which under a given bounded linear for finding common fixed points of finitely many Breg- transformation is a solution of another VIP. This problem man strongly nonexpansive operators in reflexive Banach is interesting not only from the theoretical point of view spaces. Both algorithms take into account possible compu- but also because of its potential applications. We construct tational errors. We establish two strong convergence theo- iterative algorithms that solve such problems, under rea- rems and then apply them to the solution of convex feasi- sonable conditions, in Hilbert space and then discuss spe- bility, variational inequality and equilibrium problems. cial cases, some of which are new even in Euclidean space. Shoham Sabach Technion - Israel institute of Technology Aviv Gibali [email protected] The Technion - Israel Institute of Technology aviv [email protected] OP11 Abstracts 97

CP25 CP26 Control of Variational Inequalities Eﬃcient Methods for Least-Norm Regularization

We consider the problem of ”critical excitation” (i.e., the We consider the problem: min x2 s.t. Ax − b2 ≤ , lowest energy input connecting prescribed states within a where A is an m × n matrix, b is an m × 1datavector given time span) for the variational inequality describing a containing errors (noise), and is an upper bound on the single degree of freedom elasto-plastic oscillator. This is an norm of the noise. This problem arises, for example, in optimal control problem for a non smooth state evolution. the regularization of discrete forms of ill-posed problems. We obtain Pontryagin’s necessary condition of optimality. We present two classes of methods: a Newton iteration An essential difficulty lies with the non continuity of ad- for small, dense problems, and two matrix-free algorithms joint variables. We define an algorithm which leads to the for the large-scale case. We present numerical results that optimal control. demonstrate that the new methods are accurate, efficient, and robust Janos Turi University of Texas at Dallas Marielba Rojas [email protected] Delft University of Technology [email protected] Alain Bensoussan University of Texas at Dallas Danny C. Sorensen and the Hong Kong Polytechnic University, Hong Kong Rice University [email protected] [email protected]

CP26 CP26 A Bound for Super-Resolution Power of Compres- The Sl1mmer Algorithm for Spectral Estimation sive Sensing Imaging Systems With Application to Tomographic Sar Inversion Compressive Sensing (CS) has proven a robust and high- We introduce SL1MMER, a spectral estimation algorithm resolution method for Synthetic Aperture Radar Tomogra- based on L1-norm minimisation, model order selection and phy (TomoSAR) from space. For the typical satellite orbit final parameter estimation. It combines the advantages of configurations, resolution is a crucial aspect. This paper compressive sensing with the amplitude and phase accu- quantifies the super-resolution power of CS, i.e. the min- racy of linear estimators. Our target application is differen- imum separable distance between two point scatterers, as tial Synthetic Aperture Radar (SAR) tomography. We will a function of SNR, number of measurements N, and am- also show that by means of our proposed time warp method plitude ratio of the scatterers for the typical low SNR and the tomographic imaging equation with an M-component low N cases of TomoSAR. motion model can be rewritten as an M+1-dimensional spectral estimation problem. Richard Bamler German Aerospace Center (DLR) Xiao Xiang Zhu Remote Sensing Technology Institute (IMF) Technische Universität München (TUM) [email protected] Lehrstuhl für Methodik der Fernerkundung [email protected] Xiao Xiang Zhu Technische Universität München (TUM) Richard Bamler Lehrstuhl für Methodik der Fernerkundung German Aerospace Center (DLR) [email protected] Remote Sensing Technology Institute (IMF) [email protected] CP26 Sparsity-Regularized Methods for Practical Opti- CP27 cal Imaging Decomposition Methods for Two-Stage Problems with Stochastic Dominance Constraints Traditionally, optical sensors have been designed to collect the most directly interpretable measurements possi- We consider two-stage stochastic optimization problems ble. However, recent advances in image reconstruction with risk control by a stochastic dominance constraint and compressed sensing indicate that substantial perfor- on the recourse function. We propose two decomposition mance gains may be possible in many contexts via com- methods to solve the problems and prove their convergence. putational methods. In this talk, we explore the potential Our methods exploit the decomposition structure of the of physically realizable systems for acquiring “incoherent” expected value two-stage problems and approximate the measurements. Specifically, we describe how given a fixed stochastic dominance constraints. The dominance relation size photodetector, compressive measurements with sophis- is represented by the Lorenz functions or by the expected ticated optimization algorithms can significantly increase excess functions of the random variables involved. Numer- image quality and resolution. ical results confirm the efficiency of the methods. RoummelF.Marcia Darinka Dentcheva School of Natural Sciences Department of Mathematical Sciences University of California, Merced Stevens Institute of Technology [email protected] [email protected]

Gabriela Martinez Stevens Institute of Technology 98 OP11 Abstracts

[email protected] approximation method, so called ”supporting hyperbolae”.

CP27 Olga Myndyuk A Sampled Fictitious Play Based Learning Algo- Rutgers University, RUTCOR rithm for Inﬁnite Horizon Markov Decision Pro- [email protected] cesses Andras Prekopa Using Sampled Fictitious Play (SFP) concepts, we develop Rutgers University a learning algorithm for solving discounted homogeneous Rutgers Center for Operations Research Markov Decision Problems where the transition probabil- [email protected] ities are unknown and need to be learned via simulation or direct observation of the system in real time. Thus, SFP estimates and simultaneously updates the unknown CP27 transition probabilities, optimal value and optimal action Partly Inexact Bundle Methods for Two-Stage in observed state. We prove convergence of the algorithm Stochastic Linear Programming and compare its performance with other adaptive learning methods. For two-stage stochastic linear programs, we consider partly inexact bundle methods, corresponding to a regular- Marina A. Epelman ized Benders decomposition that can handle inexactness in University of Michigan the second-stage subproblems solution. Subproblems are Industrial and Operations Engineering solved exactly only at some speciﬁc points, when inaccu- [email protected] racy is deemed too large. The remaining subproblems solution is approximated by means of previously generated Esra Sisikoglu vertices. We analyze two alternatives, derived the proximal University of Missouri and level bundle methods, and assess their performance on Industrial & Manufacturing Systems Engineering a battery of two-stage problems from the stochastic pro- [email protected] gramming literature.

Robert L. Smith Welington Oliveira Industrial and Operations Engineering Federal University of Rio de Janeiro University of Michigan [email protected] [email protected] Claudia A. Sagastizabal IMPA CP27 [email protected] Optimizing Stochastic Mixed-Integer Problems with Application in Energy Production Susana Scheimberg Federal University of Rio de Janeiro We consider a stochastic mixed-integer model, where un- Brazil certainty is described by a scenario tree. To solve this [email protected] block-structured problem, we apply a decomposition approach which exploits the problem specific structure. On this basis a branch-and-bound algorithm is used to ensure CP27 feasibility and solve the problem to global optimality. As Risk-Averse Dynamic Programming for Stochastic an application, we present a power generation problem with Shortest Path Problems fluctuating, regenerative power supply. We introduce the concept of a Markov risk measure and we Debora Mahlke, Andrea Zelmer use it to formulate a risk-averse version of the undiscounted Friedrich-Alexander-Universität Erlangen-Nürnberg stochastic shortest path problem in an absorbing Markov Lehrstuhl für Wirtschaftsmathematik chain. We derive risk-averse dynamic programming equa- [email protected], tions and we show that a randomized policy may be strictly [email protected] better than deterministic policies, when risk measures are employed. Alexander Martin University of Erlangen-Nürnberg Andrzej Ruszczynski,OzlemCavus [email protected] Rutgers University [email protected], ozlem [email protected]

CP27 Stochastic Network Design with Random Demands CP28 and Arc Capacities. Bounds for the Nonnegative Rank Using a Geo- metric Interpretation Networks are considered where the demands at the nodes and some of the arc capacities are random variables that The minimum number of nonnegative rank-one factors have joint normal distribution. A network design problem summing to a given matrix is its nonnegative rank. De- is formulated where a probabilistic constraint assures the termining this rank and the corresponding factors is com- existence of a feasible ﬂow by a large probability. The putationally diﬃcult but has many applications, e.g., in numerical solution is obtained using several methods:the graph theory, or to characterize the minimal size of any method of Prekopa that combines a cutting plane method LP extended reformulation of a combinatorial optimization with supporting hyperplane method; dynamic quadratic program. In this talk, we shed new light on this problem OP11 Abstracts 99

using a geometric interpretation involving polyhedral com- most recently proposed ones. binatorics, leading to improved upper and lower bounds. Tri-Dung Nguyen University of Southampton Nicolas Gillis School of Mathematics Université catholique de Louvain [email protected] Center for Operation Research and Econometrics [email protected] CP28 Fran¸cois Glineur Learning over Manifolds via Iterative Projection Université catholique de Louvain Center for Operations Research and Econometrics The problem of recovering an unknown signal belonging to [email protected] a manifold from linear measurements has multiple applications, one important one being imaging. In this work we introduce an algorithm known as Manifold Iterative Pro- CP28 jection to solve the problem of recovering an unknown sig- Manifold Learning by Semidefinite Facial Reduc- nal from a manifold using linear measurements. We show tion that when the linear measurement operator operates be- nignly on the manifold, the algorithm recovers the un- We propose a new semidefinite programming formulation known signal. We also extend the analysis to the case for nonlinear dimensionality reduction by manifold learn- where the signal varies slowly with time on the manifold, ing. By observing that the structure of a large chunk of and show that using the algorithm one can track the time- the data can be preserved as a whole, we are able to use varying signal. For well-behaved manifolds, random (Gaus- a recent result on semidefinite facial reduction [Krislock sian) matrices are suitable measurement operators, and the and Wolkowicz, 2010] to significantly reduce the size and sample-complexity and time-complexity can be character- the number of constraints of the semidefinite programming ized in terms of the geometric properties of the manifold. problem, allowing us to solve much larger problems than We illustrate the algorithm on several examples. previously possible. Parikshit Shah Nathan Krislock MIT INRIA Grenoble Rhône-Alpes [email protected] [email protected] Venkat Chandrasekaran Babak Alipanahi Massachusetts Institute of Technology David R. Cheriton School of Computer Science [email protected] University of Waterloo [email protected] CP29 Ali Ghodsi Extension of the Semidefinite Characterization of University of Waterloo Sum of Squares Functional Systems to Algebraic [email protected] Structures Nesterov has shown that the cone of functions that can CP28 be expressed as sums of squares of functions in a finite dimensional linear functional space can be represented by Robust Covariance Estimation Using Mathemati- positive semidefinite matrices. We extend this result to cal Programming any abstract algebraic system. Our extension is particu- The outlier detection problem and the robust covariance larly useful for formally real algebras. As a result we unify estimation problem are often interchangeable. Without some results under this framework. A noted example is outliers, the classical method of Maximum Likelihood Es- the characterization of polynomials (ordinary, exponential timation (MLE) can be used to estimate parameters of a and trigonometric) which take only positive semidefinite known distribution from observational data. When outliers values in Jordan algebras. Using Youla’s theorem we show are present, they dominate the log likelihood function caus- that such sets of polynomials are SDP-representable. We ing the MLE estimators to be pulled toward them. Many also extend our results by defining the notion of A-sdp matrices, which are matrices whose entries are from an alge- robust statistical methods have been developed to detect outliers and to produce estimators that are robust against bra (A, ). Finally, we explore some concrete applications deviation from model assumptions. However, the exist- of these characterizations in statistical function estimation ing methods suffer either from computational complexity and some problems in shape optimization. when problem size increases or from giving up desirable Farid Alizadeh properties, such as affine equivariance. An alternative ap- RUTCOR and School of Business, proach is to design a special mathematical programming Rutgers University model to find the optimal weights for all the observations, [email protected] such that at the optimal solution, outliers are given with smaller weight and can be detected. This method produces a covariance estimator that has the following prop- David Papp erties: First, it is affine equivariant. Second, it is compu- Rutgers Center for Operations Research tationally efficient even for large problem sizes. Third, it [email protected] easy to incorporate prior beliefs into the estimator by using semi-definite programming. The accuracy of this method CP29 is tested for different contamination models, including the A Geometric Theory of Barriers in Conic Opti- 100 OP11 Abstracts

mization Chemnitz University of Technology [email protected] We interpret barriers in conic optimization as Lagrangian submanifolds of some universal para-Kähler space form and Christoph Helmberg establish close links to centro-affine hypersurface geometry. TU Chemnitz As an application, we construct a universal self-concordant Germany barrier which, in contrast to the classical universal barrier, [email protected] is invariant with respect to duality and the operation of taking products of cones. This barrier corresponds to the minimal Lagrangian submanifolds, or to hyperbolic affine CP29 hyperspheres in centro-affine geometry. Riemannian Optimization for Rank-Constrained Roland Hildebrand Matrix Problems Laboratoire Jean Kuntzmann We present a Riemannian framework for solving optimiza- University Grenoble 1 / CNRS tion problems involving a rank constraint. The proposed [email protected] methods exploit that the set of n × n matrices of fixed M rank k, denoted \, form a smooth embedded submani- CP29 fold of Rn×n. This enables the use of so-called Riemannian A Globally Convergent Algorithm for Semi-Infinite optimization, the generalization of classic optimization to M Programs with an Infinite Number of Conic Con- Riemannian manifolds. Since the manifold \ is of di- straints mension O(nk), these algorithms are inherently defined on a lower dimensional search space compared to the full-rank The semi-infinite program (SIP) is normally represented case when k n. Furthermore, the framework is flexible with infinitely many inequality constraints, and has been enough to allow for second-order algorithms, precondition- much studied so far. However, there have been only a ing and multilevel optimization. We illustrate this with few studies on the SIP involving conic constraints such two applications: Lyapunov equations involving PDEs and as second-order cone constraints, even though it has im- low-rank matrix completion. portant applications such as Chebychev-like approximation and filter design. In this paper, we focus on the SIP with Bart Vandereycken infinitely many conic constraints, called the SICP for short. Katholieke Universiteit Leuven We show that, under an appropriate constraint qualifica- [email protected] tion, an optimum of the SICP satisfies the Karush-Kuhn- Tucker conditions that can be represented with only a finite subset of the conic constraints. Next we provide an CP30 algorithm for solving the SICP and show that it generates Finite Element Error Estimates on the Boundary iterates converging to a solution of the SICP under some and Its Application To Optimal Control mild assumptions. Moreover, we report some numerical experiments. Finite element error estimates in the L2-norm on the boundary are proved for elliptic boundary value problems Takayuki Okuno in polygonal domains. Local mesh grading is used in the Department of Applied Mathematics and Physics vicinity of corners with interior angle greater than 2π/3. Graduate School of Informatics Kyoto University The result is used to estimate the discretization error of t [email protected] elliptic linear-quadratic Neumann boundary control problems with pointwise inequality constraints on the control. Shunsuke Hayashi Dept of Applied Mathematics and Physics Thomas Apel Graduate School of Informatics, Kyoto University Universität der Bundeswehr München [email protected] [email protected]

Masao Fukushima Johannes Pfefferer Department of Applied Mathematics and Physics UniBw München Graduate School of Informatics Kyoto University johannes.pfeff[email protected] [email protected] Arnd Rösch University of Duisburg-Essen CP29 [email protected] Optimizing Extremal Eigenvalues of the Weighted Laplacian of a Graph CP30 In order to better understand spectral properties of the A Finite Element Method Based Numerical Algo- Laplace matrix of a graph, we optimize the edge weights so rithm for Calculus of Variations Problems Derived as to minimize the difference of the maximal and the second from Gâteaux First Variation smallest eigenvalue of the weighted Laplacian. Using a semidefinite programming formulation, the dual program A standard calculus of variations problem consists in min- allows to interpret the dual solutions living in the optimized imising a given objective functional, subject to Dirichlet eigenspaces as a graph realization. We study connections boundary conditions. Stationary points of this problem are between structural properties of the graph and geometrical obtained by imposing the Gâteaux first variation necessary properties of graph realizations. condition. A corresponding numerical scheme is attained by approximating the problem’s true solution, expressing Susanna Rei the interpolant as a linear combination of cubic spline ba- OP11 Abstracts 101

sis functions. Different numerical integration rules for the and the knot locations are optimized simultaneously. To integrals intervening in Gâteaux first variation expression illustrate and compare both approaches, time optimal in- are applied. puts are calculated for an overhead crane.

Ana Garcia-Bouso Wannes Van Loock Universidad Rey Juan Carlos Katholieke Universiteit Leuven Statistics and Operations Research Department Department of Mechanical Engineering, division PMA [email protected] [email protected]

Alberto Olivares, Ernesto Staﬀetti Goele Pipeleers, Jan Swevers Universidad Rey Juan Carlos (Madrid) Katholieke Universiteit Leuven Statistics and Operations Research Department [email protected], [email protected], ernesto.staﬀ[email protected] [email protected]

CP30 CP31 Multivariate Shape-Constrained Estimation Using Solving DFO Non Convex Subproblems with a Polynomial Splines Global Optimizer We present a solution to multivariate function estimation The SQA (Sequential Quadratic Approximation) is a con- problems with shape constraints on the estimator. We ap- strained derivative-free algorithm developed at IFPEN. In ply tools from polynomial programming and decomposition the minimization stage, quadratic subproblems, not nec- methods. The estimator is a multivariate spline, for which essarily convex, subjected to bound and quadratic con- most natural shape constraints are intractable, hence we straints are solved using a standard SQP algorithm. Due consider tractable restrictions involving weighted-sum-of- to the non-convexity issue, subproblem solutions computed squares cones. The size of these problems often makes the through the local SQP algorithm may only be local solu- direct solution of the models impossible, hence the need to tions. This motivates our choice to use GloptiPoly, a global combine the conic programming technique with decompo- optimizer for polynomial optimization for solving quadratic sition methods. subproblems. In order to integrate GloptiPoly as the subproblem solver, it was tested for some quadratic problems David Papp of the Hock Shitkowski benchmark. Then, it was plugged Rutgers Center for Operations Research in SQA as the quadratic subproblem solver for the Moré& [email protected] Wild benchmark. Finally, GloptiPoly was used for solving a real engine calibration problem. Comparisons of Glop- Farid Alizadeh tiPoly with standards SQP methods and multistart ones RUTCOR and School of Business, will be given for the Moré & Wild benchmark and the cal- Rutgers University ibration problem, respectively. [email protected] Frédéric Delbos IFP Energies Nouvelles CP30 [email protected] Numerical Explorations of Benford Distributed Random Variables Laurent Dumas Université de Versailles A random variable is Benford distributed if the occur- [email protected] rence frequency of its most significant digit is p(d)= log10(1 + 1/d). Using numeric data from 2-d relativistic Eugenio Echague gas simulations, we observed that the generalized relativis- IFP energies nouvelles tic equipartition terms are Benford distributed. They are [email protected] also base and scale invariant. Because the equipartition terms are nonlinear functions of non-uniform distributed random variables, we expect that the exponentiation the- CP31 orem of Adhikari and Sarkar be extended to non-uniform Estimating Parameters in Optimal Control Models probability distribution functions as well. We consider numerical methods for identifying models that Constantin N. Rasinariu,AzarKhosravani describe dynamical processes that can be assumed to be Department of Science and Mathematics optimal, such as gaits of cerebral palsy patients. This Columbia College Chicago leads to challenging parameter estimation problems whose [email protected], [email protected] constraints are constrained optimal control problems. We present a multiple shooting approach to discretize this hi- CP30 erarchical optimization problem and discuss methods to treat the resulting problem: a Gauß-Newton approach, a Optimal Input Design with B-Splines: Linear Ver- bundle method, and a derivative-free technique. Numerical sus Semidefinite Programming results are provided.

Input design is considered for linear controllable systems Kathrin Hatz by means of a B-spline parametrization of the flat output. Interdisciplinary Center for Scientific Computing (IWR) Actuator and state constraints are satisfied continuously University of Heidelberg, Germany in time by either conservative linear or exact semidefinite [email protected] constraints on the spline coefficients resulting in a linear or semidefinite program in which both the spline coefficients Johannes Schloeder 102 OP11 Abstracts

Interdisciplinary Center for Scientific Computing (IWR) with time-stepping approaches. University of Heidelberg [email protected] Mihai Anitescu, Jungho Lee, Lois Curfman McInnes, Todd Munson Hans Georg Bock Argonne National Laboratory IWR, University of Heidelberg Mathematics and Computer Science Division [email protected] [email protected], [email protected], [email protected], [email protected] Sven Leyffer Argonne National Laboratory Barry F. Smith leyff[email protected] Argonne National Lab MCS Division [email protected] CP31 Optimal Control of Hydroforming Processes Lei Wang University of Michigan We consider optimal control problems for quasi-static [email protected] elastoplasticity with linear hardening. As a first step derivative free optimization algorithms were used to control the blank holder force and the fluid pressure, which are MS1 typical control variables. The commercial FEM-software Extended Mathematical Programming: Multi- ABAQUS is invoked for the simulations. Because of the agent Modeling Simplified huge computational effort of the simulation, optimization algorithms based on reduced models are under investiga- We present the GAMS Extended Mathematical Program- tion. Numerical results for the hydroforming process of ming framework (EMP). This new tool enables multi-agent sheet stringers will be presented. models to be formulated in terms of individual agents, e.g., optimization/complementarity models, and the structure Daniela Koller and relationships that connect them, e.g. via a Nash game TU Darmstadt or a leader-follower structure. The JAMS solver automati- [email protected] cally reformulates the problem to create an equivalent but tractable model, solves it, and brings back the solution to Stefan Ulbrich the EMP framework. Several examples are furnished for Technische Universitaet Darmstadt illustration. Fachbereich Mathematik [email protected] Steven Dirkse GAMS Development Corp. Washington DC CP31 [email protected] Derivative-free Methods for Large Nonlinear Data Assimilation Problems Michael C. Ferris University of Wisconsin To estimate the state of the ocean and of the atmosphere, Department of Computer Science very large nonlinear least-squares problems have to be [email protected] solved. These problems involve a model operator which integrates a set of partial differential equations describing Jan-H. Jagla, Alex Meeraus the evolution of the system. Evaluating the derivatives is GAMS Development Corp. challenging, as one needs to compute the Jacobian of the Washington DC model operator and its transpose, which implies the deriva- [email protected], [email protected] tion of a tangent linear and adjoint codes. In this talk, we present a derivative-free alternative based on the solution of subproblems in well-choosen small subspaces. MS1 On C-stationarity for Parabolic MPECs Patrick Laloyaux University of Namur A constraint-relaxation technique for a class of optimal [email protected] control problems for parabolic variational inequalities is considered. The relaxed problem can be treated by well- known results from optimization in Banach space and MS1 yields, upon passing to the limit in the relaxation parame- A Variational Inequality Approach for the Evolu- ter, a weak form of C-stationarity for the original problem. tion of Heterogeneous Materials The theoretical results are illustrated by numerical tests. We aim to predict the evolution of microstructure in het- Michael Hintermueller erogeneous materials, as appears, for example, in mate- Humboldt-University of Berlin rials that are submitted to radiation for long periods of [email protected] time. Such phenomena can be modeled by phase field approaches with double obstacle potentials. Such formulations result in differential variational inequalities. We dis- MS1 cuss approaches for solving the large-scale variational in- Semismooth New- equalities that result from spatial discretization combined ton Methods for Quasi-Variational Inequalities of OP11 Abstracts 103

Elliptic Type and Applications Greuet, Feng Guo and Lihong Zhi.

A problem arising from a nonlinear elliptic quasi- Mohab Safey El Din variational inequality (QVI) with gradient constraints is UPMC, Univ Paris 6 considered. We address the existence of solutions based on [email protected] a penalization approach and a fixed point iteration without resorting to Mosco convergence. The numerical approximation of the solution is done by developing a semismooth MS3 Newton strategy in combination with the fixed point itera- Implementation of Nonsymmetric Interior-point tion in function space. Numerical examples related to the Methods for Linear Optimization Over Sparse Ma- p-Laplacian and a superconductivity model will be treated. trix Cones Carlos N. Rautenberg We describe implementations of nonsymmetric interior- Department of Mathematics and Scientific Computing point methods for linear optimization over two types of Karl-Franzens University of Graz sparse matrix cones: the cone of positive semidefinite ma- [email protected] trices with a given sparsity pattern, and the cone of com- pletable matrices. The implementations take advantage of fast sparse matrix algorithms for evaluating the associated MS2 logarithmic barriers and their derivatives. We present nu- Polynomial Descriptions of Special Classes of Semi- merical results of an implementation of an interior-point algebraic Sets algorithm based on these techniques with applications to robust quadratic optimization problems. Bosse, Groetschel and Henk asked whether an arbitrary d-dimensional polytope can be described by d polynomial Martin S. Andersen inequalities, i.e., in the form p1 ≥ 0,...,pd ≥ 0, where University of California, Los Angeles p1,...,pd are d-variate polynomials. This question is an- Electrical Engineering Department swered in positive (in a joint work with Ludwig Bröcker) [email protected] and the corresponding theorem is also extended to the case of unbounded polyhedra. In this talk I will sketch the proof Joachim Dahl and present some related problems. MOSEK Aps joachim@mosek.com Gennadiy Averkov University of Magdeburg [email protected] Lieven Vandenberghe University of California Los Angeles MS2 [email protected] Spectrahedra and Determinantal Representations of Polynomials MS3 Spectrahedra are the feasible sets of semidefinite optimiza- Semidefinite Programming Algorithm for Dis- tion problems. It is an important problem to characterize tributed Stability Analysis sets that are spectrahedra. The algebraic problem behind this geometric question is to represent polynomials as de- We investigate stability of uncertain large-scale intercon- terminants of linear matrix polynomials. I will discuss pos- nected systems using μ-analysis. The interconnections are itive and negative results concerning this problem. few. This means that the system matrix relating input to output signals is sparse. The μ-analysis problem can be Tim Netzer formulated as a semidefinite programming (SDP) problem University of Leipzig involving the system matrix. We will present results on [email protected] how this SDP problem can be solved efficiently in a distributed fashion.

MS2 Sina Khoshfetrat Pakazad Algebraic Certificates for Global Optimization and Division of Automatic Control Generalized Critical Values Linköping University [email protected] We consider the problem of computing algebraic certificates certifying lower bounds for the global infimum a mul- Anders Hansson tivariate polynomial subject to equality constraints satisfy- Division of Automatic Control ing transversality assumptions. Following a previous work Linköping University of Demmel, Nie and Sturmfels involving sums-of-squares [email protected] decompositions modulo gradient ideals, Nie has recently established the existence of SOS certificates modulo gen- Anders Rantzer eralized gradient ideals and convergence results in the case Lund University where the infimum is a minimum. Following an idea intro- [email protected] duced by Schweighofer which consists in considering larger varieties than the ones defined by gradient ideals, we pro- Martin S. Andersen vide existence results for algebraic certificates certifying University of California, Los Angeles lower bounds of the considered global infimum even when Electrical Engineering Department it is not a minimum. This is joint work with Aurelien [email protected] 104 OP11 Abstracts

MS3 Sandia National Laboratories Parallel Multilevel Computing in SDPARA for [email protected] Large-scale Semideﬁnite Programming Herbie Lee We discuss a hybrid MPI and multi-threading parallel com- University of California, Santa Cruz putation on multi-core CPUs. It is employed in the lat- Dept. of Applied Math and Statistics est version 7.3.1 of SDPARA (a parallel version of SDPA). [email protected] SDPARA 7.3.1 adopts a new storage scheme to reduce of memory consumption and to derive an ideal load balance Katie Fowler among processors. Numerical results show that this par- Clarkson University allel scheme provides an astonishing speed up on SDPs. [email protected]

Kazuhiro Kobayashi MS4 National Maritime Research Institute [email protected] Application of Optimization-Under-Uncertainty in the Design of Pump-and-Treat Systems Makoto Yamashita Pump-and-treat systems can prevent groundwater contam- Tokyo Institute of Technology inant migration and candidate systems are typically evalu- Dept. of Mathematical and Computing Sciences ated via groundwater models. Such models should be cali- [email protected] brated so that parameter uncertainties can be incorporated into subsequent simulation-based optimization. Numerous Katsuki Fujisawa calibration procedures have been proposed, yielding vary- Department of Industrial and Systems Engineering ing expressions of parameter uncertainty. A series of nu- Chuo University merical experiments were performed utilizing optimization- [email protected] under-uncertainty to design a remedial system for groundwater contamination. Results indicate that alternative approaches for parameter estimation can significantly influ- MS4 ence optimal system design. Enhanced Hospital Resource Management using Anticipatory Policies in Online Dynamic Multi- L. Shawn Matott, Philip Sheffield objective Optimization University of Waterloo [email protected], psheffi[email protected] Evolutionary algorithms are well-suited to solve both multi-objective and dynamic optimization problems. Studying problems that are multi-objective and dynamic MS4 is only rather recent. An important problem difficulty (in Post-inference Optimization in a Multi-scale practice) is that decisions taken now have future conse- Bayesian Setting quences. We tackle this issue by optimizing policies that are well-designed for the problem at hand with a multi- Simulations in difficult optimization problems often depend objective evolutionary algorithm and apply this approach on the solution of an inference problem. An example is the to a complex, real-world optimization problem, namely the permeability field in a well placement design problem which management of resources in a hospital. is often derived from pressure or saturation measurements. Furthermore, uncertainty in the inverse solution can have a Peter Bosman significant impact on the optimization. Incorporating this Centrum Wiskunde & Informatica (CWI) during optimization is difficult and we present a method to (Centre for Mathematics and Computer Science) take advantage of structure in a Bayesian inference problem [email protected] during the optimization. Matthew Parno,YoussefM.Marzouk MS4 Massachusetts Institute of Technology Calculation of Uncertainty Information During [email protected], [email protected] Calibration The problem of calibration of a computer simulator in- MS5 volves determining the optimal values of several tuning in- Feasibility Pump Heuristics for Nonconvex MINLP put variables that, when combined with input variables matching known conditions, produce output values that Finding feasible solutions of Mixed Integer Nonlinear Pro- match real observed data. At its heart is the comparison gramming (MINLP) problems is crucial to the performance of experimental data and simulation results. Complicat- of any branch-and-bound MINLP solver. We describe a ing this comparison is the fact that both data sets contain variant of the Feasibility Pump heuristic, which was in- uncertainties which must be quantified in order to make troduced for Mixed Integer Linear Programming (MILP) reasonable comparisons. Therefore, UQ techniques must problems and extended to MINLP. Our implementation be applied to identify, characterize, reduce, and, if possi- takes advantage of an LP relaxation of the MINLP prob- ble, eliminate uncertainties. In this talk, we will discuss lem that can be dynamically refined. We provide compu- an approach to calibration which combines Bayesian sta- tational results based on Couenne, an Open Source solver tistical models and derivative-free optimization in order to for non-convex MINLP problems. monitor sensitivity information throughout the calibration process. Pietro Belotti Clemson University Genetha Gray [email protected] OP11 Abstracts 105

Timo Berthold the large amount of CPU power available in order to reduce Zuse Institute Berlin the size of the enumeration tree, studying their eﬀect and Takustr. 7 14195 Berlin discussing their applicability in the single-processor case. [email protected] Our focus will be on bound tightening techniques. If time permits, we will also discuss branching.

MS5 Giacomo Nannicini MINOTAUR: A Solver for MINLPs Carnegie Mellon University Tepper School of Business In this talk we describe MINOTAUR, a solver that we are [email protected] developing for general MINLPs. MINOTAUR provides a ﬂexible framework for implementing a variety of techniques Pietro Belotti for relaxing, branching, cutting, searching and other meth- Clemson University ods that are necessary for solving MINLPs. We describe [email protected] some new techniques that we have developed and compare their performance to existing ones. MINOTAUR is also ca- Jon Lee pable of identifying certain basic problem structures that IBM T.J. Watson Research Center can be exploited eﬀectively. We describe these methods [email protected] also.

Sven Leyffer Jeff Linderoth Argonne National Laboratory University of Wisconsin-Madison leyff[email protected] Dept. of Industrial and Sys. Eng [email protected] Ashutosh Mahajan Argonne National Laboratory Francois Margot [email protected] Carnegie Mellon University Tepper School of Business Todd Munson [email protected] Argonne National Laboratory Mathematics and Computer Science Division Andreas Waechter [email protected] Thomas J. Watson Research Center [email protected]

MS5 Linear and Nonlinear Inequalities for a Nonsepara- MS6 ble Quadratic Set Nested Multigrid for Optimal Control of Time- periodic Parabolic PDEs We describe some integer-programming based approaches for finding strong inequalities for the convex hull of a We present a nested multigrid (mg) method to solve opti- quadratic mixed integer nonlinear set containing two in- mal control problems with time-periodic parabolic PDEs. teger variables that are linked by linear constraints. This The method relies on the reduction of the first order op- study is motivated by the fact that such sets appear can timality conditions to a Fredholm integral equation of the be defined by a convex quadratic program, and therefore second kind which is solved by the outer mg method. In strong inequalities for this set may help to strengthen the every outer iteration a space-time mg approach of the first formulation of the original problem. Some of the inequali- kind is applied as inner mg method for the evaluation of ties we define for this set are linear, while others are non- the integral kernel to solve for the state and adjoint state. linear (specifically conic). The techniques used to define strong inequalities include not only ideas related to recent perspective reformulations of MINLPs, but also disjunctive Dirk Abbeloos and lifting arguments. Initial computational tests will be Department of Computer Science presented. K. U. Leuven [email protected] Hyemin Jeon, Jeffrey Linderoth University of Wisconsin-Madison Moritz Diehl [email protected], [email protected] K.U.Leuven [email protected] Andrew Miller Institut de Mathématiques de Bordeaux Michael Hinze France Universität Hamburg [email protected] Department Mathematik [email protected]

MS5 Stefan Vandewalle A Computational Study on Branching and Bound Department of Computer Science Tightening Techniques for MINLPs Katholieke Universiteit Leuven [email protected] Within the context of developing a parallel Branch-and- Bound solver for nonconvex MINLPs, we perform a computational investigation of branching and bound tightening techniques. We propose new methods that try to exploit 106 OP11 Abstracts

MS6 such approximations, as well as techniques for aggregating Multi-level Optimization Algorithms for PDE- information from different length-scales for the purposes of constrained Problems Arising in Materials Design optimization. Motivated by gas storage in nanoporous materials, we con- Robert M. Lewis sider a novel class of optimization problems. Applications College of William and Mary require a specified rate of charge and discharge which is [email protected] facilitated by creating channels of various widths. The objective is to minimize the total volume of the channels. The physics changes as scale is reduced and must be correct on MS7 all scales to solve the problem. We describe extensions to Infeasibility Detection in Nonlinear Programming the multi-grid optimization method to solve such multiscale problems. We address the deficiencies of current nonlinear optimization software with respect to infeasibility detection. In Paul Boggs particular, it is suggested in this talk that algorithms be Sandia National Lab reworked and reanalyzed so that, if given an infeasible [email protected] problem, useful information is returned to the user efficiently. We also propose our own approaches for sequen- David M. Gay tial quadratic optimization and interior-point methods that AMPL Optimization LLC provide the same convergence guarantees as contemporary University of New Mexico methods, but also provide fast local convergence guaran- [email protected] tees for infeasible problems. Frank E. Curtis,HaoWang Robert M. Lewis Industrial and Systems Engineering College of William and Mary Lehigh University [email protected] [email protected], [email protected]

Stephen G. Nash George Mason University MS7 Systems Engineering & Operations Research Dept. Active Set Strategies for the Gradient Projection [email protected] Algorithm

When solving a nonlinear programming problem using the MS6 gradient projection method, we often need to project a Nonlinear Domain Decomposition Methods for the vector into the linearized constraints. Active set strategies Solution of Constrained Nonlinear Programming for solving the projection problem are examined, including Problems the dual active set algorithm.

The parallel numerical solution of realistic problems, such William Hager as large-deformation contact between an elastic body and University of Florida a rigid obstacle, gives rise to nonlinear programming prob- hager@ufl.edu lems (NLPs) which will reliably be solved employing globalization strategies. In this talk, we will consider an extension to the concept of globalization strategies, nonlin- MS7 early preconditioned globalization strategies, and focus on A Robust Algorithm for Semidefinite Program- the application of such strategies to the multiscale solu- ming tion of large-scale NLPs arising from the discretization of constrained PDEs. Current successful methods for solving semidefinite programs, SDP, use symmetrization and block elimination Christian Gross steps that create ill-conditioning in the Newton equations. Universita’ della Svizzera Italiana We derive and test a backwards stable primal-dual interior- Institute of Computational Science point method for SDP that avoids the ill-conditioning. Our [email protected] algorithm is based on a Gauss-Newton approach that allows for a preconditioned (matrix-free) iterative method Rolf Krause for finding the search direction at each iteration. Universita’ della Svizzera Italiana Henry Wolkowicz [email protected] University of Waterloo Department of Combinatorics and Optimization MS6 [email protected] Approximation and Correction Techniques for De- sign of a Nanoporous Material Xuan Vinh Doan C&O Department We discuss approaches to the hierarchical design of a University of Waterloo nanoporous material for energy storage. The structure and [email protected] physical nature of the material varies on different length- scales. The system can be approximated using a small Serge Kruk number of decision variables, which makes it possible to Department of Mathematics and Statistics consider algebraic approximations of the objective and con- Oakland University, Rochester, MI straints in the resulting optimization problem. We discuss [email protected] OP11 Abstracts 107

MS7 and its integration into the presented one-shot procedure. A Trust Region Algorithm for Inequality Con- strained Optimization with a New Scaling Tech- Nicolas R. Gauger nique Department of Mathematics and CCES RWTH Aachen University In this paper, we propose a trust region algorithm for in- [email protected] equality constrained optimization with a new scaling technique. The scaling is derived by considering the special case of bound constraints, where the scaling matrix de- MS8 pends on the gradients of the objective function and the Avoiding Mesh Deformations in Boundary Shape distances to the bounds. Global convergence results of the Optimization algorithm are presented. We propose an approach to boundary shape optimization Xiao Wang in which the geometry is represented through varying coef- Inst of Comp Math & Sci/Eng. AMSS ficients in the governing equation. Our method constructs Chinese Academy of Sciences raster representations of the geometries, which circumvents [email protected] the need for re-meshing and enables flexible choices of admissible designs. The method has been assessed on an Ya-Xiang Yuan acoustic optimization problem, using a shape parameteri- Chinese Academy of Sciences zation that is difficult to employ with traditional methods, Inst of Comp Math & Sci/Eng, AMSS for which it generated visually smooth devices with favor- [email protected] able acoustic properties. Fotios Kasolis MS8 Department of Computing Science Umea University, Sweden Efficient Aerodynamic Design [email protected] We present our methods for aircraft aerodynamic shape optimization based on Computational Fluid Dynamics. The Eddie Wadbro examples of applications are total drag minimization at Department of Computing Science cruise flight conditions, which involves resolving the prop- Ume˚aUniversity agation of disturbances in the boundary layer, and lift max- [email protected] imization at landing and take-off, which requires solutions of the Reynolds Averaged Navier-Stokes equations. We Martin Berggren also present our investigations in static aeroelastic opti- Department of Computing Science, Umea University mization based on CFD. [email protected] Olivier G. Amoignon FOI-Swedish Defence Research Agency MS8 [email protected] Aerodynamic Design based on Shape Calculus

Ardeshir Hanifi, Jan Pralits, Daniel Skoogh, Fredrik Shape optimization based on the Hadamard form of the Berefelt, Lars Tysell, Adam Jirasek, Mattias Chevalier shape derivative is considered. The Hadamard form pro- FOI vides an analytically exact surface formulation of the gradi- ardeshir.hanifi@foi.se, [email protected], ent, allowing shape optimization without the need to com- [email protected], [email protected], pute so called mesh sensitivities. Thus, shape optimization [email protected], [email protected], based on a first optimize then discretize fashion is enabled, [email protected] where e.g. all mesh surface nodes can be used as design unknowns with next to no additional costs. Furthermore, approximations to shape Hessians are considered, thereby cre- MS8 ating a shape one-shot optimization method. The talk con- An Adaptive One-Shot Approach for Aerodynamic culdes with the optimization of a blended wing-body air- Shape Optimization craft using 113,956 surface nodes as the shape unknowns. We focus on so-called one-shot methods and their applications to aerodynamic shape optimization, where the Stephan Schmidt governing equations are the Navier-Stokes or Reynolds- University of Trier averaged Navier-Stokes (RANS) equations. We constrain [email protected] the one-shot strategy to problems, where steady-state solutions are achieved by pseudo-time stepping schemes. The one-shot optimization strategy pursues optimality simul- MS9 taneously with the goals of primal and adjoint feasibility. 4D Imaging using Optimal Transport and Sparsity To exploit the domain specific experience and expertise in- Concepts vested in the simulation tools, we propose to extend them in an automated fashion by the use of automatic differentia- We present models and efficient algorithms for 4D recon- tion (AD). First they are augmented with an adjoint solver struction in biomedical imaging using optimal transport to obtain (reduced) derivatives and then this sensitivity in- and sparsity concepts. Standard reconstruction methods formation is immediately used to determine optimization do not incorporate time dependent information or kinetics. corrections. Finally, we discuss how to use the adjoint so- This can lead to deficient accuracy particularly at object lutions also for goal-oriented error estimation and how to boundaries, e.g. at cardiac walls. We discuss constraint make use of the resulting error sensor for mesh adaptation optimization models combining reconstruction techniques 108 OP11 Abstracts

known from inverse problems, spatio-temporal regulariza- ling reentry phenomena. tion and mass conservation. The numerical realization is based on multigrid preconditioned Newton-SQP with fil- Karl Kunisch tered line-search and efficient operator splitting techniques Karl-Franzens University Graz with parallelization. Dynamic large-scale biomedical data Institute of Mathematics and Scientific Computing illustrate the performance of our methods. [email protected]

Christoph Brune Nagaiah Chamakuri, Marcus Wagner Institute for Computational and Applied Mathematics Karl-Franzens University Graz University of Muenster, Germany [email protected], [email protected] [email protected]

Martin Burger Institute for Numerical and Applied Mathematics MS9 University of Muenster Large Scale Optimization Problems in Medical [email protected] Imaging

Eldad Haber This talk presents a brief introduction to image registration Department of Mathematics and introduces the FAIR (Flexible Algorithms for Image The University of British Columbia Registration) package for a numerical solution using MAT- [email protected] LAB. Moreover, a new component which enables mass preserving registration is discussed. The mass preserving registration is based on a new and thorough discretization of MS9 the determinant of the Jacabian and the co-factor matrix. Numerical Optimization for Constrained Image Numerical results related to fast magnetic resonance imag- Registration with Application to Medical Imaging ing sequences are presented. Image registration is a technique aimed at establishing Jan Modersitzki meaningful correspondences between image voxels from dif- University of Lübeck ferent perspectives. It is an essential tool for various ap- Institute of Mathematics and Image Computing plications in medicine, geosciences, and other disciplines. [email protected] However, obtaining plausible deformations is a complex task as often transformations are required to be locally Lars Ruthotto invertible or even more challenging, are required to bound Institute of Mathematics and Image Computing volume changes within a reasonable range. In this work, [email protected] solutions to the registration problem were obtained by directly imposition of a volume constraint upon each voxel in a discretized domain. This study focuses on the devel- MS10 opment of an efficient and robust numerical algorithm and Conservation Laws Coupled with Ordinary Differ- in particular, the application of an augmented Lagrangian ential Equations method with a multigrid as preconditioner. We demonstrate that this combination yields an almost optimal solver This presentation describes some recent results concerning for the problem. the basic well posedness theory of systems consisting of conservation laws coupled with ordinary differential equa- Raya Horesh tions. Several examples will be considered in more detail Institute of Mathematics and its Applications and numerical result will be presented. University of Minnesota [email protected] Rinaldo M. Colombo University of Brescia Department of Mathematics Eldad Haber [email protected] Department of Mathematics The University of British Columbia [email protected] MS10 Feedback Stabilization for the Gas Flow in Net- Jan Modersitzki works University of Lübeck Institute of Mathematics and Image Computing The control of the gas flow in pipe networks plays an im- [email protected] portant role for the supply with natural gas. The gas flow through pipelines can be modeled by the isothermal Eu- ler equations with friction, which are a hyperbolic 2x2- MS9 PDE-system of balance laws. We present recent results Optimal Control of the Bidomain Equations on the boundary feedback stabilization of the isothermal Euler equations locally around a given stationary state. Well-posedness of the bidomain equations is investigated The stabilization methods are based upon transformation for several well-established ionic current models. Optimal to Riemann invariants and upon Lyapunov functions. The control problems are formulated to influence the extra and feedback laws guarantee an exponential decay of the Lya- intracellular potentials by means of extracellular applied punov functions with time. current. Optimality conditions are derives rigorously. Nu- merical examples illustrate, for the two dimensional case, Markus Dick the feasibility of dampening excitation waves and control- Universität Erlangen-Nürnberg OP11 Abstracts 109

Dept. of Mathematics the literature. [email protected] Elvira Hernandez Departamento de Matemática Aplicada MS10 UNED Madrid On Control and Controllability of Systems of Non- [email protected] linear Conservation Laws Miguel Sama We give an overview on optimal control and controllabil- Universidad Nacional de Educación a Distancia ity for one–dimensional hyperbolic systems. We present a [email protected] short summary of theoretical as well as numerical results. Applications towards network flows and controllability re- Luis Rodriguez-Marin sults on those are given. UNED Michael Herty [email protected] RWTH Aachen Universtiy Department of Mathematics MS11 [email protected] Fenchel-Rockafellar Duality for Set-valued Prob- lems via Scalarization MS10 New Fenchel-Rockafellar type duality results for set-valued Numerical Approximation of Optimal Control optimization problems are proven. The image space is a Problems for Discontinuous Solutions of Hyper- complete lattice of subsets of a preordered locally convex bolic Conservation Laws space. The proof consists of characterizing set-valued func- We analyse the convergence of discrete approximations to tions by families of extended real-valued ones and apply- optimal control problems for discontinuous solutions of ing the scalar result. As corollaries, calculus rules for set- hyperbolic conservation laws. Building on a sensitivity valued conjugates are shown. Applications to vector op- and adjoint calculus for the optimal control problem we timization problems are given by introducing a set-valued show that an appropriate discretization by finite difference dual. schemes with sufficient numerical viscosity at shock dis- Carola Schrage continuities leads to convergent approximations of the lin- Institute for Mathematics earized and the adjoint equation and thus to convergent Martin-Luther-University Halle-Wittenberg gradient approximations of the cost functional. Hence, ef- [email protected] ficient optimization methods are applicable. We present numerical results. Andreas H. Hamel Stefan Ulbrich Yeshiva University Technische Universitaet Darmstadt Department of Mathematical Sciences Fachbereich Mathematik [email protected] [email protected] MS11 MS11 Lagrange Necessary Conditions for Pareto Mini- Set-Valued Optimization Revisited: From Minimal mizers in Asplund Spaces and Applications Points to Lattice Solutions In this talk, new necessary conditions for Pareto mini- Motivated by duality issues, set-valued optimization prob- mal points of sets and Pareto minimizers of constrained lems have been studied since the 1980ies. Later, Tanaka multiobjective optimization problems are established with- et al. initiated solution concepts based on set relations. out the sequentially normal compactness property and the Recently, it has been shown that set-valued optimization asymptotical compactness condition imposed on closed and (only) admits a complete (duality) theory if lattice exten- convex ordering cones. Our approach is based on a versions both of image and pre-image space are used. This sion of a separation theorem for nonconvex sets and the theory matches the needs of applications in finance: opti- subdifferentials of vector-valued and set-valued mappings. mization problems for set-valued risk measures in markets Furthermore, applications in mathematical finance and ap- with transaction costs. The talk will be a guided tour proximation theory are discussed. through these subjects. Christiane Tammer Andreas H. Hamel Faculty of Sciences III, Institute of Mathematics Yeshiva University University of Halle-Wittenberg Department of Mathematical Sciences [email protected] [email protected] Bao Q. Truong Mathematics and Computer Science. Department MS11 Northern Michigan University About Set-valued Optimization via the Set Scheme [email protected]

The goal of this talk is to explore solution concepts in set-valued optimization and to clarify some links between MS11 them. Exactly, we study some criteria of solution asso- Extended Pareto Optimality in Multiobjective ciated to a set-valued optimization problem and we give optimality conditions by revising several existing results in 110 OP11 Abstracts

Problems University of Zurich [email protected] This talk presents new developments on necessary conditions for minimal points of sets and their applications to Bernd Kummer deriving refined necessary optimality conditions in general Humboldt-University of Berlin models of set-valued optimization with geometric, func- [email protected] tional, and operator constraints in finite and infinite dimensions. The results obtained address the new notions of extended Pareto optimality with preference relations MS12 generated by ordering sets satisfying the local asymptotic Introduction to Mathematical Programs with Cone closedness property instead of that generated by convex Complementarity Constraints andclosedcones.Inthiswayweunifyandextendmost of the known notions of efficiency/optimality in multiob- Optimization problems involving symmetric positive jective models and establish optimality conditions that are semidefinite matrix variables,i.e., Semidefinite programs new even in standard settings. Our approach is based on (SDPs), are well studied in engineering control and struc- advanced tools of variational analysis and generalized dif- tural mechanics. Mathematical programs with semidefi- ferentiation. nite complementarity constraints are nonconvex optimization problems arising, e.g., as inverse problems when the Bao Q. Truong forward model is an SDP. After penalizing the complemen- Mathematics and Computer Science. Department tarity/orthogonality constraint,a nonconvex problem with Northern Michigan University both matrix and vector variables and constraints remains. [email protected] Stationarity conditions are analyzed and the penalty formulation is solved for an application from structural opti- Boris Mordukhovich mization. Wayne State University Department of Mathematics Daniel Ralph [email protected] University of Cambridge Dept. of Engineering & Judge Institute of Management [email protected] MS12 On Calmness Conditions in Convex Bilevel Pro- Michal Kocvara gramming School of Mathematics University of Birmingham We compare two well-introduced calmness conditions in [email protected] the context of convex bilevel programming, namely partial calmness related to the value function approach and calmness of the solution set to the lower level problem under MS12 linear perturbations of the lower level objective. Both con- On the Derivation of Optimality Conditions for El- cepts allow to derive first order necessary optimality condi- liptic MPECs via Variational Analysis tions. They differ, however, in their assumptions and in the resulting optimality conditions. We illustrate by theoreti- An elliptic MPEC is any mathematical program whose fea- cal results as well as by the example of a dicretized obstacle sible set is governed by an elliptic variational inequality. control problem that partial calmness is too restrictive in After demonstrating new results concerning the contingent general. derivative of the solution mapping associated with the variational inequality, we derive an upper approximation of Rene Henrion the Fréchet normal cone of the feasible set. This leads to Weierstrass Institute optimality conditions resembling S-stationarity conditions. Berlin, Germany The strength of the results are then demonstrated by con- [email protected] sidering a model from the theory of elastoplasticity. Thomas M. Surowiec Thomas M. Surowiec Department of Mathematics Department of Mathematics Humboldt University of Berlin Humboldt University of Berlin [email protected] [email protected]

MS12 MS13 Handling Set Constraints in Variational Problems Semideﬁnite Programming and Occupation Mea- like Usual Inequalities sures for Impulsive Control of Dynamical Systems

In many optimization and variational problems, abstract The problem of dynamical systems control can be ap- set-constraints of the type h(x) ∈ C, C polyhedral, ap- proached constructively via occupation measures charac- pear. Such set constraints are often handled separately in terised by their moments satisfying semidefinite program- its algebraic form when deriving stability (and solvability) ming constraints. This allows for a genuine primal ap- conditions, since standard constraint qualifications may fail proach focusing on systems trajectories, in contrast with to hold. We show how such problems can be rewritten in more classical dual approaches based on Lyapunov or simi- traditional inequality and equation form in such a way that lar energy functionals satisfying Hamilton-Jacobi-Bellman results on stability of solutions and feasible points for the partial differential equations. We survey recent achieve- related classical models can be directly applied. ments in the area, with a focus on the design of impulsive control laws with application in satellite orbital transfer Diethard Klatte problems. Joint work with Denis Arzelier, Mathieu Claeys OP11 Abstracts 111

and Jean-Bernard Lasserre. Faculty of Economic Sciences Tilburg University Didier Henrion [email protected] LAAS-CNRS, University of Toulouse, & Faculty of Electrical Engineering, Czech Technical University [email protected] MS13 P´olya’s Theorem and Optimization

MS13 Let R[X]:=R[X1,...,Xn]. Pólya’s Theorem says that if Algebraic Certificates for Linear Matrix Inequali- a form (homogeneous polynomial) p ∈ R[X] is positive on ties and Semidefinite Programming the standard n-simplex Δn, then for sufficiently large N N all the coefficients of (X1 + ···+ Xn) p are positive. In Given linear matrix inequalities (LMIs) L1 and L2 it is 2001, Powers and Reznick gave a bound on the N needed, natural to ask: in terms of the degree of p, the coefficients, and minimum 1. when does one dominate the other, that is, does of p on . This quantitative Pólya’s Theorem has many ap- L1(X) 0implyL2(X) 0? plications, in both pure and applied mathematics. For example, it is an ingredient in the degree bound for Putinar’s 2. when are they mutually dominant, that is, when do Positivstellensatz given by J. Nie and M. Schweighofer in they have the same solution set? 2007. This degree bound gives information about the con- In this talk we describe a natural relaxation of an LMI, vergence rate of Lasserre’s procedure for optimizaiton of based on substituting matrices for the variables xj .With a polynomial subject to polynomial constraints. In joint this relaxation, the domination questions (1) and (2) have work with M. Castle and B. Reznick, we extend the quanti- elegant answers. Assume there is an X such that L1(X) tative Pólya’s Theorem to forms which are allowed to have and L2(X) are both positive definite, and suppose the pos- zeros on Δn. We give a complete characterization of forms itivity domain of L1 For our “matrix variable’ relaxation for which the conclusion of Pólya’s Theorem holds (with a positive answer to (1) is equivalent to the existence of “positive on Δn” relaxed to “nonnegative on Δn”), and a matrices Vj such that bound on the N. We discuss these results and connections with optimization using Lasserre’s method. ∗ ∗ L2(x)=V1 L1(x)V1 + ···+ Vμ L1(x)Vμ. (1) Victoria Powers As for (2), L1 and L2 are mutually dominant if and only if, Emory University up to certain redundancies, L1 and L2 are unitarily equiva- [email protected] lent. Particular emphasis will be given to the case of empty LMI sets {X | L(X) 0}. MS14 An Introduction to a Class of Matrix Cone Pro- We shall explain how to derive a polynomial sos version of gramming the Farkas lemma for linear programming thus giving rise to a polynomial size infeasibilty certificate for semidefinite In this talk, we introduce a class of matrix cone program- programs (SDP). The talk is based on joint works with ming (MCP), which consists of linear conic programming M. Schweighofer,andJ.W. Helton and S. McCullough;see problems whose conic constraints involve the epigraphs of e.g. http://arxiv.org/abs/1003.0908 l1, l∞, spectral or nuclear matrix norms. We study several important properties, including its closed form solution, Igor Klep calm Bouligand-differentiability and strong semismooth- University of California, San Diego ness, of the metric projection operator over these matrix [email protected] cones. These properties make it possible to design some efficient algorithms such as augmented Lagrangian methods, MS13 to solve MCP problems. Error Bounds for Sums of Squares Relaxations of Chao Ding Some Polynomial Optimization Problems National University of Singapore [email protected] We consider semidefinite programming relaxations for polynomial optimization problems based on sums of squares of polynomials and the dual relaxations based on Defeng Sun moment matrices. In particular, we give new error bounds Dept of Mathematics for optimization over the hypercube for the hierarchy of re- National University of Singapore laxations corresponding to Schmüdgen’s Positivstellensatz. [email protected] These bounds are explicit and sharpen an earlier result of Schweighofer (2004). This is based on joint work with E. de Kim-Chuan Toh Klerk. We also discuss recent bounds of Karlin, Mathieu National University of Singapore and Nguyen (2011) for the case of a linear objective and Department of Mathematics and Singapore-MIT Alliance a unique linear constraint (corresponding to the knapsack [email protected] problem) and show that they extend to a block-diagonal version of Lasserre’s hierarchy. MS14 Monique Laurent Iteration-Complexity of Block-Decomposition Al- Tilburg University gorithms and the Alternating Minimization Aug- CWI, Amsterdam mented Lagrangian Method [email protected] In this talk, we discuss the complexity of block- Etienne Klerk, de decomposition methods for solving monotone inclusion 112 OP11 Abstracts

problems consisting of the sum of a continuous monotone National University of Singapore map and a point-to-set maximal monotone operator with a Department of Mathematics and Singapore-MIT Alliance separable two-block structure. As a consequence, we derive [email protected] complexity results for alternating minimization augmented Lagragian methods for for solving block-structured convex optimization problems. Moreover, we also apply our re- MS15 sults to derive new methods and corresponding complexity Optimizing over the Complement of Ellipsoids results for the monotone inclusion problem consisting of the sum of two maximal monotone operators. We describe continuing work related to the optimization of convex functions over the complement of a union of ellip- Renato C. Monteiro soids. This arises in several practical nonconvex optimiza- Georgia Institute of Technology tion problems, and is related to several fundamental prob- School of ISyE lem areas in optimization. Joint work with Alex Michalka [email protected] and Mustafa Tural.

Benar Svaiter Daniel Bienstock IMPA Columbia University IEOR and APAM Departments Rio de Janeiro, Brazil IEOR Department [email protected] [email protected]

MS14 MS15 An Inexact Interior Point Method for L1- Pooling Problems with Binary Variables regularized Sparse Covariance Selection The pooling problem consists of finding the optimal quan- Sparse covariance selection (CSC) problems can be for- tity of final products to obtain by blending different compo- mulated as log-determinant optimization problems with sitions of raw materials in pools. We study a generalization large number of linear constraints. We propose a cus- of the problem where binary variables are used to model tomized inexact interior-point algorithm for solving such fixed costs associated with using a raw material in a pool. large scale problems. At each iteration, we solve the large We derive four classes of strong valid inequalities, that can and ill-conditioned linear system of equations by an it- be separated in polynomial time, and dominate classic flow erative solver using highly effective preconditioners con- cover inequalities. Successful computational results are re- structed based on the special problem structures. Nu- ported. merical experiments on synthetic and real CSC problems Claudia D’Ambrosio show that our algorithm can outperform other existing al- University of Bologna gorithms. DEIS Kim-Chuan Toh [email protected] National University of Singapore Department of Mathematics and Singapore-MIT Alliance Jeff Linderoth [email protected] University of Wisconsin-Madison Dept. of Industrial and Sys. Eng Lu Li [email protected] ANZ Bank [email protected] James Luedtke University of Wisconsin-Madison Department of Industrial and Systems Engineering MS14 [email protected] A Proximal Point Algorithm for Log-Determinant Optimization with Group Lasso Regularization MS15 We propose a practical proximal point algorithm for solv- Computationally Effective Disjunctive Cuts for ing large scale log-determinant optimization problem with Convex Mixed Integer Nonlinear Programs group Lasso regularization and linear equality constraints. At each iteration, as it is difficult to update the primal We discuss computationally effective methods for generat- variables directly, we solve the dual problem by a Newton- ing disjunctive inequalities for convex mixed-integer non- CG method, and update the primal variables by an explicit linear programs (MINLPs). Computational results indi- formula based on the computed dual variables. We present cate that disjunctive inequalities have the potential to numerical results to demonstrate that the proposed algo- close a significant portion of the integrality gap for convex rithm is efficient, especially when high accuracy is required. MINLPs and to be as effective for solving convex MINLPs as they have been for solving mixed-integer linear pro- Junfeng Yang grams. Nanjing University [email protected] Mustafa Kilinc University of Wisconsin-Madison Defeng Sun Dept. of Industrial and Sys. Eng Dept of Mathematics [email protected] National University of Singapore [email protected] Jeff Linderoth University of Wisconsin-Madison Kim-Chuan Toh Dept. of Industrial and Sys. Eng OP11 Abstracts 113

[email protected] Optimization

Jim Luedtke We investigate two approaches to the solution of topology University of Wisconsin-Madison optimization problems using decomposition of the compu- Dept. of Industrial and Sys. Eng tational domain. The first approach is based on a two [email protected] stage algorithm; a block Gauss-Seidel algorithm is combined with a first order method guaranteeing convergence. The second approach uses the semidefinite programming MS15 formulation of the problem. We replace the original large Lifted Inequalities for Mixed Integer Nonlinear matrix constraint by several smaller constraints. This leads Sets with Special Structure to a significant improvement in efficiency.

Lifting is the process of converting a seed inequality valid Michal Kocvara for a restriction of the set to the unrestricted set. We apply School of Mathematics lifting to specially-structured nonlinear sets. For mixed- University of Birmingham binary bilinear knapsacks, we derive inequalities that are [email protected] not easily obtained using IP techniques. For mixed-binary bilinear covers, we obtain facet-deﬁning inequalities that Masakazu Kojima generalize well-known inequalities for certain ﬂow mod- Tokyo Institute of Technology els. Finally, we derive valid nonlinear inequalities for dis- [email protected] junctive sets by projecting families of parameterized linear lifted inequalities. James Turner School of Mathematics Mohit Tawarmalani University of Birmingham, UK Purdue University [email protected] [email protected]

Jean-Philippe Richard MS16 Department of Industrial and Systems Engineering Inexact Solution of NLP Subproblems in MINLP University of Florida [email protected]fl.edu We investigated how the outer approximation method and the generalized Benders decomposition method are affected Kwanghun Chung when the NLP subproblems are solved inexactly. We show Center for Operations Research and Econometrics that the cuts in the master problems can be changed to in- [email protected] corporate the inexact residuals, still rendering equivalence and finiteness in the limit case. Some numerical results will be presented to illustrate the behavior of the methods MS16 under NLP subproblem inexactness. The Lifted Newton Method for Nonlinear Opti- Luis N. Vicente,MinLi mization University of Coimbra The lifted Newton method is designed for the solution of [email protected], [email protected] nonlinear optimization problems that have objective and constraint functions with intermediate variables. Introduc- MS16 ing these as additional degrees of freedom into the original problem offers more freedom for initialization and often, Fast NLP Solvers for MINLP faster contraction rates are observed. An algorithmic trick Branch-and-bound is the underlying framework for all effi- allows us to perform each lifted Newton iteration at al- cient mixed-integer optimization solvers. In the linear case most no additional computational cost compared to a non- (MILP), significant speed improvements have been made lifted Newton iteration. We discuss under which conditions using strong-branching and diving techniques, because LP faster local quadratic convergence for lifted iterations can solvers can handle problem changes consisting of changing be expected, and demonstrate the speedup due to the lifted just one bound very effectively. In this talk, we explore Newton method at a large PDE parameter estimation ex- whether similar improvements can be made in the nonlin- ample. Part of the material was published in [Albersmeyer ear (MINLP) context. and Diehl, The Lifted Newton Method and Its Application in Optimization. SIAM Journal on Optimization (2010) Andreas Waechter 20:3,1655-1684]. Thomas J. Watson Research Center [email protected] Moritz Diehl K.U.Leuven [email protected] MS17 A Linearized Model for Dynamic Positron Emis- Jan Albersmeyer sion Tomography previously at IWR, Uni Heidelberg [email protected] Dynamic Positron Emission Tomography allows monitoring physiological processes within the body that can be described by kinetic parameters. However, recovery of these MS16 parameters often requires the solution of complex and non- Domain Decomposition Methods for Structural linear operator equations. A variational framework is introduced that allows to promote sparsity of minimizers with 114 OP11 Abstracts

respect to a temporal exponential basis. Jean-Christophe Pesquet, Nelly Pustelnik LIGM Martin Benning Universit´eParis-Est Institute for Computational and Applied Mathematics [email protected], University of Muenster [email protected] [email protected]

MS17 MS17 ImageRestorationinthePresenceofNon-additive Exact Relaxation to Bounded Variation Problems Noise In this talk, we consider a class of problems given by the We are concerned with the restoration of (blurred) images constrained minimization problems of the form corrupted by multiplicative or Poisson noise. On the one hand, we propose alternating direction methods of multi- min F (v)+ G(v)udx+ TV(u), (2) pliers for minimizing an I-divergence/TV functional which (u,v)∈BV (Ω;{0,1})×V Ω is related to both multiplicative and Poisson noise. On the other hand, we suggest novel nonlocal filters for removing V→ where F : R is a (sequentially)weakly lower√ semicon- multiplicative noise. To this end, a suitable similarity mea- tinuous functional bounded below and G : V→L (⊗)isa sure has to be found for defining the weights occurring in strongle continuous nonlinear operator for some p>1. The these filters in dependence on the noise statistics. model covers a lot of applications, such as the total variation (ROF) model for binary image restoration, Mumford- Gabriele Steidl Shah model for image segmentation, minimal compliance Institute of Mathematics und Computer Science in topology optimization, etc. In order to solve these bi- Universitaet Mannheim, Germany nary constrained problems, we introduce the exact relax- [email protected] ation of (1) and give an efficient algorithm based on the Fenchel dual technique. Moreover, we show that the min- Tanja Teuber imizers of (1) are able to be obtained by taking level sets University of Mannheim, Germany of minimizers of the relaxation. Dept. of Mathematics and Computer Science [email protected] Yiqiu Dong Institute of Biomathematics and Biometry Helmholtz Zentrum München MS18 [email protected] Optimal Treatment Strategies Determined by Ki- netic Equations Michael Hintermueller Humboldt-University of Berlin Using a Boltzmann transport model, we consider the ques- [email protected] tion of optimal treatment strategies in radiation therapy. We derive optimality conditions for an optimal control Martin Burger problem with space-dependent constraints on the size of Institute for Numerical and Applied Mathematics the dose and present numerical results. University of Muenster Richard C. Barnard [email protected] RWTH Aachen University Center of Computational Engineering Sciences MS17 [email protected] Dynamic PET Reconstruction using Parallel ProX- imal Algorithm MS18 We propose to extend a recent convex optimization ap- Title Not Available at Time of Publication proach based on the Parallel ProXimal Algorithm to im- TBA. prove the estimation at the voxel level in dynamic Positron Emission Tomography (PET) imaging. The criterion to be Günter Leugering minimized is composed with a Kullback-Leibler divergence University Erlangen-Nuremberg as a data fidelity term, an hybrid regularization (defined Institute of Applied Math. as a sum of a total variation and a sparsity measure), and [email protected] a positivity constraint. The total variation is applied to each temporal frame and a wavelet regularization is considered for the space+time data. This allows us to smooth MS18 the wavelet artifacts introduced when the wavelet regular- Relaxation Schemes and Optimal Control ization is used alone. The proposed algorithm is evaluated on simulated and real dynamic fluorodeoxyglucose (FDG) Relaxation schemes are well-known and easy to implement brain data. discretization schemes for systems of conservation or balance laws. Hereby, the original (nonlinear) system of bal- Caroline Chaux ance laws is replaced by a linear system of double size, UniversitéParis-Est called the relaxation system. Using asymptotic analysis [email protected] it can be shown that the relaxation system is well-posed if the new system matrix satisfies the so-called subchar- Claude Comtat acteristic condition. Under this assumption a solution to SHFJ, CEA the relaxation system is known to converge to a solution [email protected] of the original system. Furthermore, using IMEX-schemes OP11 Abstracts 115

for the time integration of the numerical scheme, it can niques, including new approaches. be shown that the discretized relaxation system converges to a discretization of the limit equations. To provide con- Arnold Neumaier sistent schemes for optimal control, we derive conditions University of Vienna such that the discrete adjoint of the relaxation system is Department of Mathematics a valid discretization of the continuous adjoint relaxation [email protected] system in the context of smooth solutions. Furthermore, we prove that the discretization of the adjoint relaxation system converges to a discretization of the adjoint limit MS19 equation. This discretization then turns out to be the ad- An Active Set Trust-region Method for Derivative- joint of the discretized limit equation. free Nonlinear Bound-constrained Optimization Veronika Schleper We consider an implementation of a recursive model- University of Stuttgart based active-set trust-region method for solving bound- Institute of applied Analysis and Numerical Simulation constrained nonlinear non-convex optimization problems [email protected] without derivatives using the technique of self-correcting geometry proposed in [Scheinberg and Toint, 2009]. Con- sidering an active-set method in model-based optimization MS18 creates the opportunity of saving a substantial amount of H1-controllability of Nonlinear Conservation Laws function evaluations. It allows to maintain much smaller interpolation sets while proceeding optimization in lower We present a relaxation scheme to the optimal control of dimensional subspaces. The resulting algorithm is shown nonlinear hyperbolic systems, in particular the control of to be numerically competitive. Euler flows in gas dynamics. The relaxation approximation under consideration has a linear transport part combined Anke Troeltzsch with a stiff source term. We discuss how the relaxation CERFACS scheme can be applied to controllability problems involving Toulouse, France nonlinear hyperbolic equations. We present some numeri- [email protected] cal results. Philippe L. Toint Sonja Steffensen University of Namur RWTH Aachen University [email protected] Dept. of Mathematics [email protected] Serge Gratton ENSEEIHT, Toulouse, France MS19 [email protected] Derivative Free Optimization Method with Non Linear Constraints: Some Industrial Applications MS20 Derivative free optimization takes place in various applica- Computational Experience tion fields and often requires dedicated techniques to limit with Copositive Programming-Based Approxima- the number of evaluations of the usually time consuming tions of the Stability Number simulator. We propose the Sequential Quadratic Approx- We present recent advances in the approximate computa- imation method (SQA) based on a trust region method tion of the stability number of a graph using the doubly with quadratic interpolation models. Its efficiency is illus- nonnegative relaxation introduced by Lovasz, McEliece, trated on two industrial applications: an inverse problem Rodemich, Rumsey, and Schrijver. Two possible improve- for reservoir characterization which requires an adapted ments to handle its quadratic number of constraints are implementation for least-square problems and an engine discussed. First, we consider reducing the size of the calibration problem with derivative free constraints. original relaxation by a partial aggregation of its equal- Delphine Sinoquet ity constraints. Second, we relax the doubly nonnega- IFP Energies nouvelles tive relaxation to a semidefinite relaxation and discuss [email protected] a new cutting-plane method to handle the nonnegativity constraints more efficiently. The approach is based on a new interior-point algorithm that selects relevant sets of Delbos Frédéric, Langouët Hoël inequalities dynamically while exploiting the capability to IFPEN warm start problems after updates without the need to [email protected], [email protected] restart or to modify previous iterates. We present computational results that quantify the computational benefit MS19 from each of these two techniques. Challenges in Derivative-free Optimization Miguel F. Anjos Mathematics and Industrial Engineering & GERAD Derivative-free optimization made substantial progress Ecole´ Polytechnique de Montréal since the times of the Nelder-Mead simplex method. But [email protected] several important challenges remain. In particular, there is a need for improvements in at least three areas where current methods frequently perform poorly: – the large-scale Alexander Engau case (50 or more variables), – the noisy case (uncertainties University of Colorado, Denver, USA. of 10% or more), – the constrained case (tight black box [email protected] constraints). This talk reviews some of the better tech- 116 OP11 Abstracts

Immanuel Bomze nodes and yields very tight bounds. University of Vienna [email protected] Veronica Piccialli Università degli Studi di Roma Tor Vergata [email protected] MS20 Second Order Motivated Scaling Approaches for Franz Rendl the Spectral Bundle Method Universitat Klagenfurt Institut fur Mathematik The spectral bundle method is a nonsmooth first order [email protected] solver for semidefinite optimization over large sparse matrices. Oustry outlined how to combine first order approaches Angelika Wiegele with the second order approach of Overton and Womer- Alpen-Adria-Universit{ sly. We report on work in progress towards using second } order models in a large scale setting for practical scaling ”a t Klagenfurt variants within the spectral bundle package “ConicBundle” Institut f. Mathematik and present first numerical results. [email protected]

Christoph Helmberg MS21 TU Chemnitz Germany Minty Variational Principle for Set-valued Varia- [email protected] tional Inequalities It is well known that a solution of a Minty scalar variational Michael L. Overton inequality of differential type is a solution of the related New York University optimization problem, under lower semicontinuity assump- Courant Instit. of Math. Sci. tion. This relation is known as ”Minty variational princi- [email protected] ple”. In this presentation we study this principle in the vector case for an arbitrary ordering cone and a non differ- Franz Rendl entiable objective function. Further, we extend the Minty Alpen-Adria Universitaet Klagenfurt variational principle to set-valued variational inequalities. Austria [email protected] Giovanni Crespi UniversitédelaVallée d’Aoste [email protected] MS20 Semidefinite Relaxations of Ordering Problems Ivan Ginchev, Matteo Rocca University of Insubria Ordering problems assign weights to each ordering and ask Department of Economics to find an ordering of maximum weight. The linear order- [email protected], [email protected] ing problem is wells tudied, with exact solution methods based on polyhedral relaxations. The quadratic ordering problem does not seem to have attracted similar attention. MS21 We present a systematic investigation of semidefinite opti- On the Notion of Approximate Strict Solution in mization based relaxations for the quadratic ordering prob- Set-valued Optimization via the Set Solution Cri- lem, extending and improving existing approaches. We terion show the efficiency of our relaxations by providing computational experience on a variety of problem classes. This talk is concerned with set-valued optimization problems. A new concept of approximate strict solution based Philipp Hungerlaender, Franz Rendl on coradiant sets and the set optimality criterion is intro- Alpen-Adria Universitaet Klagenfurt duced. Then, the behavior of these approximate solutions Austria when the error tends to zero is studied. Finally, some exis- [email protected], [email protected] tence results are obtained through scalarization processes.

MS20 César Gutiérrez A Semidefinite Relaxation for Sparse Max-Cut Departamento de Matemática Aplicada Problems Universidad de Valladolid [email protected] We investigate semidefinite relaxations of the Max-Cut problem, which are formulated in terms of the edges of the graph, thereby exploiting the (potential) sparsity of the Bienvenido Jimenez problem. We show how this is related to higher order lift- Universidad Nacional de Educacion a Distancia ings of Anjos and Wolkowicz and Lasserre. Contrary to the [email protected] basic semidefinite relaxation, which is based on the nodes of the graph, the present formulation leads to a model which Vicente Novo is significantly more difficult to solve. To solve the result- Universidad Nacional de Educación a Distancia ing SDP we developed an algorithm where we factorize [email protected] the matrix in the dual SDP and apply an augmented La- grangian algorithm to the resulting minimization problem. Lionel Thibault We present computational results that indicate that this D model is manageable for sparse graphs on a few hundred ’epartement des Sciences Math OP11 Abstracts 117

’ematiques Department of Mathematics Universit University of Regensburg ’e de Montpellier II [email protected] [email protected]

MS22 MS21 Optimal Shape Design Subject to Variational In- Bishop-Phelps Cones equalities For Bishop-Phelps (BP) cones various properties are pre- The shape of the free boundary arising from the solution sented in normed spaces. Representations of the interior of a variational inequality is controlled by the shape of the and the interior of the dual cone of a BP cone are given. domain where the variational inequality is defined. Shape A characterization of the reflexivity of a Banach space is and topological sensitivity analysis is performed for the formulated using these cones. For an arbitrary cone with obstacle problem and for a regularized version of its primal- a closed bounded base it is shown how an equivalent norm dual formulation. The shape derivative for the regularized can be constructed so that this cone is representable as a problem is defined and converges to the solution of a linear BP cone. problem. These results are applied to the electrochemical machining problem. Johannes Jahn Department of Mathematics Antoine Laurain University of Erlangen-Nuremberg Karl-Franzens University of Graz, Austria [email protected] [email protected]

Truong Xuan Duc Ha Institute of Mathematics of Hanoi MS22 [email protected] A Parabolic MPEC Approach to the Calibration of American Options Pricing

MS21 An inverse problem in the pricing of American options is Conic Regularization for Some Optimization Prob- considered. The problem is formulated as an MPEC problems lem in function space. First-order optimality conditions of C-stationarity-type are derived. The discrete optimality In recent years new optimality conditions, by means of mul- system is solved numerically by using an active-set-Newton tiplier rules, were obtained for abstract optimization prob- solver with feasibility restoration. lems in function spaces where the associated ordering cone of has a nonempty interior. However, it turns out that the Hicham Tber multipliers for these problems belong to non-regular spaces Department of Mathematics of measures. One of the essential requirement of these stud- School of Science and Technology Beni-Mellal ies is the validity of a Slater’s type constraint qualification. [email protected] It is known that Slater’s type constraint qualification is a stringent condition and it does not hold for many im- Michael Hintermueller portant cases of interest. In this talk, we will discuss a Humboldt-University of Berlin new conical regularization technique that gives optimality [email protected] conditions without requiring any Slater’s type constraint qualification. The Henig dilating cones is the basic technical tool for this study. Finite element discretization of MS22 the dilating cone will be discussed and numerical examples Optimal Control of Mixed Variational Inequalities will be presented. In this talk some theoretical and numerical aspects on the Akhtar A. Khan optimal control of variational inequalities of the second Rochester Institute of Technology kind will be presented. A special kind of regularizing func- [email protected] tions with an active-inactive set structure will be introduced and its importance for the obtention of sharp neces- Miguel Sama sary conditions will be highlighted. In addition, the design Universidad Nacional de Educación a Distancia of second order numerical methods, both globally and lo- [email protected] cally convergent, for the solution of the control problems will be discussed.

MS22 Juan Carlos de los Reyes Escuela Politécnica Nacional Quito Optimal Control of the Cahn-Hilliard Variational Quito, Ecuador Inequality [email protected] An optimal control problem governed by Allen-Cahn variational inequality is studied. These problems are phase MS23 field versions of optimal control problems for interfaces and free boundaries. First order optimality conditions are de- Approximating Convex Hulls of Planar Quartics rived by using a penalization/relaxation technique. We Planar quartics are among the simplest examples of al- also use ideas of Hintermüller/Kopacka concerning station- gebraic sets for which computing the convex hull is non- arity concepts for MPECs in function spaces. trivial, and for which applying sums of squares tech- Hassan Farshbaf-Shaker 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- Numerical Optimization stood. In this talk we will use these objects as an illustration of the techniques, giving a brief survey of what is We present a proximal bundle method for convex nondif- known and showing, for this particular case, a nice geomet- ferentiable minimization where the model is a piecewise ric characterization of the ﬁrst sums of squares relaxations. quadratic convex approximation of the objective function. Unlike standard bundle approaches, the model only needs to support the objective function from below at a prop- Joao Gouveia erly chosen subset of points, as opposed to everywhere. University of Washington We provide the convergence analysis for the algorithm, [email protected] with a general form of master problem which combines features of trust-region stabilization and proximal stabilization, taking care of all the important practical aspects MS23 such as proper handling of the proximity parameter and A New Look at Nonnegativity and Polynomial Op- of the bundle of information. Numerical results are also timization reported.

We provide a new characterization of nonnegativity of a Annabella Astorino continuous function f on a closed and non necessarily com- Istituto di Calcolo e Reti ad Alte Prestazioni - CNR pact set K of Rn.Whenf is a polynomial this characteri- [email protected] zation specializes and provides a hierarchy of nested outer approximations (Ck) of the convex cone C(K; d) of polyno- Antonio Frangioni mials of degree at most d, nonnegative on K. Each convex Dipartimento di Informatica cone Ck is a spectrahedron in the coefficients of f with no University of Pisa lifting. In addition, for a fixed known f,checkingmem- [email protected] bership in Ck reduces to solving a generalized eigenvalue problem for which specialized softwares are available. Manlio Gaudioso Jean B. Lasserre Dipartimento di Elettronica Informatica e Sistemistica LAAS CNRS and Institute of Mathematics Università della Calabria, Italia [email protected] [email protected]

Enrico Gorgone MS23 Dipartimento di Elettronica Informatica e Sistemistica The Central Path in Linear Programming Università della Calabria [email protected] The central curve of a linear program consists of the central paths for optimizing over any region in the arrangement of constraint hyperplanes. We determine the degree, genus MS24 and defining ideal of this curve, thereby answering a 1989 New Discrete Gradient Limited Memory Bundle question of Bayer and Lagarias. Refining work of Dedieu, Method for Derivative Free Nonsmooth Optimiza- Malajovich and Shub, we bound the total curvature of cen- tion tral paths, and we construct instances with many inflection points. Joint work with Jesus DeLoera and Cynthia Vin- A new derivative free method is developed for solving zant. unconstrained nonsmooth optimization problems. The method is based on the discrete gradient method by Bernd Sturmfels Bagirov et.al. and the limited memory bundle method by University of California , Berkeley the author. The new method uses a bundle of discrete gra- [email protected] dients to approximate the subdifferential of a nonsmooth function. The size of the bundle is kept low by the procedure similar to the limited memory bundle method. More- MS23 over, the limited memory approach is used to limit the Convergence Theory of Successive Convex Re- needed number of operations and the storage space. The laxation Methods for Optimization over Semi- comparison to some existing methods is given. Algebraic Sets Napsu Karmitsa I will discuss various techniques (new and old) used in con- Department of Mathematics vergence proofs for successive convex relaxation methods University of Turku applied to optimization problems expressed as maximiza- napsu@karmitsa.fi tion of a linear function over a finite set of polynomial inequality constraints. I will focus on convergence rates and Adil Bagirov specially structured nonconvex optimization problems. CIAO, School of ITMS, The University of Ballarat Levent Tuncel [email protected] University of Waterloo Dept. of Combinatorics and Optimization [email protected] MS24 Science Fiction in Nonsmooth Optimization MS24 In the 1970’s Lemaréchal found that a quasi-Newton Piecewise Quadratic Approximations in Convex method for smooth optimization performed well on some nonsmooth test functions. This was confirmed by Lewis and Overton in 2008. In the 1980’s Lemaréchal said that OP11 Abstracts 119

“Superlinear convergence in nonsmooth optimization is sci- we construct primal optimal solutions with tensor liftings ence fiction”. We discuss the current state of affairs for of a class of linear programming bounds for the stability rapid convergence, based on the U-Hessian of Lemaréchal, number of a graph. Oustry and Sagastizábal, and give a BFGS VU-algorithm that appears to show the achievement of science fiction. Hongbo Dong Department of Mathematics Robert Mifflin University of Iowa Washington State University [email protected] miffl[email protected]

Claudia Sagastizábal MS25 CEPEL (Electric Energy Research Center) Projections onto the Copositive Cone, and Appli- Brazil cations [email protected] In this talk we present an algorithm for the projection of a matrix A onto the copositive cone C.ByprojectingA onto MS24 a sequence of polyhedral inner and outer approximations C C The Proximal Chebychev Center Cutting Plane Al- of , we can approximate the projection of A onto with gorithm for Convex Additive Functions arbitrary precision. Furthermore we consider projections onto the completely positive cone, which is the dual cone The recent algorithm based on Chebychev centers proposed of C, and we discuss two applications. recently [Math. Prog., 119, pp. 239-271, 2009] for convex nonsmooth optimization, is extended to the case of Julia Sponsel additive functions. We highlight aspects where this ex- University of Groningen tension differs from the aggregate case. We consider two [email protected] different nonlinear multicommodity flows applications in telecommunications to assess the method. The numerical Mirjam Duer experiments also include some comparison with a proximal TU Darmstadt bundle algorithm. [email protected]

Adam Ouorou France Telecom R&D-Orange Labs MS25 [email protected] Computational Experience with Polyhedral Ap- proximations of Copositive Programs MS25 Relying on the previous results in the literature, the author Separation and Relaxation for Completely Positive recently proposed hierarchies of inner and outer polyhedral Matrices approximations of the copositive cone. Using these approximations, two sequences of increasingly sharper lower and The cone C of completely positive (CP) matrices is im- upper bounds can be computed for the optimal value of portant for globally solving many NP-hard quadratic pro- a copositive program. Under mild assumptions, both se- grams. We construct a conceptual separation algorithm for quences converge to the optimal value in the limit. We C based on optimizing over smaller CP matrices, which in present computational results in an attempt to shed light particular yields a concrete separation algorithm for 5 × 5 on the performance of these approximations in practice. CP matrices. The separation algorithm also motivates a new class of tractable relaxations for C,eachofwhichim- E. Alper Yildirim proves a standard polyhedral-semidefinite relaxation. The Koc University relaxation technique can further be applied recursively to [email protected] obtain a new hierarchy of relaxations, and for constant recursive depth, the hierarchy is tractable. MS26 Samuel Burer New Inequalities for Piecewise Linear Optimization University of Iowa and Mixed-integer Nonlinear Programming Dept of Management Sciences [email protected] We give new valid inequalities for the piecewise linear optimization (PLO) knapsack polytope. Then, we present Hongbo Dong the results of our extensive computational study on their Department of Mathematics use on branch-and-cut to solve PLO, as well as nonconvex University of Iowa nonliear and mixed-integer nonlinear programming [email protected] Ismael De Farias, Rajat Gupta, Ernee Kozyreff Texas Tech MS25 [email protected], [email protected], ernee.kozyreff@ttu.edu Symmetric Tensor Approximation Hierarchies for the Completely Positive Cone Ming Zhao In this work we construct two tensor-structured approxi- SAS mation hierarchies for the completely positive cone. We [email protected] show they correspond to dual cones of two known approximation hierarchies for the copositive cone, one being polyhedral and the other being semidefinite. As an application, 120 OP11 Abstracts

MS26 Rutherford Appleton Laboratory Strong Polyhedral Relaxations for Multilinear Pro- [email protected] grams Philippe L. Toint We study methods for obtaining polyhedral relaxations of The University of Namur problems containing multiple multilinear terms. The goal Department of Mathematics is to obtain a formulation that is more compact than the [email protected] convex hull formulation, but yields tighter relaxations than the term-by-term or McCormick relaxation. We present promising computational results for an approach based on MS27 grouping the variables into subsets that cover all multilin- On Sequential Optimality Conditions for Con- ear terms in the problem. strained Optimization

James Luedtke This talk is based in joint papers with R. Andreani, G. University of Wisconsin-Madison Haeser and B. F. Svaiter. We are concerned with first- Department of Industrial and Systems Engineering order necessary conditions for smooth constrained opti- [email protected] mization. A feasible point satisfies a sequential condition if there exists a sequence that converges to it and fulfills Jeff Linderoth some computable property. These conditions are useful to University of Wisconsin-Madison analyze algorithms and to provide stopping criteria. Usu- Dept. of Industrial and Sys. Eng ally, sequential conditions exhibit an Approximate-KKT [email protected] form and are satisfied by local minimizers independently of constraint qualifications. Mahdi Namazifar University of Wisconsin-Madison Jose Mario Martinez [email protected] IMECC-UNICAMP [email protected]

MS26 MS27 On the Chvatal-Gomory Closure of a Compact Convex Set Cubic Regularization Algorithm and Complexity Issues for Nonconvex Optimization In this talk, we show that the Chvatal-Gomory closure of any compact convex set is a rational polytope. This We consider regularization methods for the nonconvex un- resolves an open question of Schrijver 1980 for irrational constrained and convexely constrained optimization prob- polytopes, and generalizes the same result for the case of lems. We review known convergence results their remark- rational polytopes (Schrijver 1980), rational ellipsoids (Dey able complexity properties, that is the number of function and Vielma 2010) and strictly convex bodies (Dadush, Dey evaluations that are needed for the algorithm to produce and Vielma 2010). an epsilon-critical point. We also discuss the complexity of the steepest-descent and Newton’s methods in the uncon- Juan Pablo Vielma strained case and report surprising conclusions regarding University of Pittsburgh their relative complexity. We also indicate why the cubic [email protected] relaxation method (ARC) is remarkable and how results obtained for this method may be extended to ﬁrst-order Daniel Dadush, Santanu S. Dey and DFO algorithms. Georgia Institute of Technology Philippe L. Toint [email protected], [email protected] The University of Namur Department of Mathematics MS27 [email protected] Towards Optimal Newton-Type Algorithms for Nonconvex Smooth Optimization Coralia Cartis University of Edinburgh We consider a general class of second-order methods for School of Mathematics unconstrained minimization that includes Newton’s, inex- [email protected] act linesearch, cubic regularization and some trust-region variants. For each algorithm in this class, we exhibit an Nick Gould example of a bounded-below objective with Lipschitz con- Numerical Analysis Group tinuous gradient and Hessian such that the method takes Rutherford Appleton Laboratory at least O(−/∈) function-evaluations to drive the gradi- [email protected] ent below . Thus cubic regularization has (order) optimal worst-case complexity amongst the methods in this class. MS27 Coralia Cartis Back to the Future: Revisiting the Central Path University of Edinburgh School of Mathematics Since the mid-1980s—the beginning of modern interior- [email protected] point methods—the central path has played a major conceptual and computational role in nonlinear optimization. Nick Gould But the same objects (curves of local minimizers of penalty Numerical Analysis Group and barrier functions) were studied during the 1960s and 1970s under diﬀerent names. Reverting temporarily to the OP11 Abstracts 121

earlier interpretations, this talk will examine interesting MS28 and useful properties of the central path that have tended The Use of a Generalized Fisher Equation and to be overlooked in recent years, including the implications Global Optimization in Chemical Kinetics of a non-tangential approach to the solution and implicit identification of the active set. A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth Margaret H. Wright to its variance. The GFE is an exact mathematical result New York University that has been widely used in population dynamics and ge- Courant Institute of Mathematical Sciences netics, where it originated. Here we demonstrate that the [email protected] GFE can also be useful in other fields, specifically in chemistry, with models of chemical reaction systems for which the mechanisms and rate coefficients correspond reason- MS28 ably well to experiments. The discrepancy of experimental Control of Glucose Balance in ICU Patients data with the GFE can be used as an optimization criterion for the determination of rate coefficients in a given Consistent tight blood sugar control in critically ill patients reaction mechanism. We illustrate this approach with two has proven elusive. Properly accounting for the satura- examples, the chloriteiodide and the Oregonator systems. tion of insulin action and reducing the need for frequent measurements are important aspects in intensive insulin John Ross therapy. In this talk we present the composite metabolic Stanford University model Glucosafe by Pielmeier et al. (Computer Methods Palo Alto, CA and Programs in Biomedicine, 97:211-222, 2010) that inte- [email protected] grates models and parameters from normal physiology and accounts for the reduced rate of glucose gut absorption and Alejandro F. Villaverde, Julio R. Banga saturation of insulin action in patients with reduced insulin IIM-CSIC sensitivity. It is a system of non-linear ordinary differen- Vigo, Spain tial equations with randomly perturbed parameters whose [email protected], [email protected] optimal control is of main focus. Nicole Marheineke Federico Moran, Sara Vazquez FAU Erlangen-Nuernberg Universidad Complutense de Madrid [email protected] Madrid, Spain [email protected], [email protected] Thomas Cibis TU Kaiserslautern / Fraunhofer ITWM MS29 [email protected] Direct MultiSearch: A New DFO Approach for Multiple Objective Functions Ulrike Pielmeier Aalborg University DMS is a novel derivative-free algorithm for multiobjective [email protected] optimization, which does not aggregate any of the objective functions. Inspired by the search/poll paradigm of direct-search, DMS uses the concept of Pareto dominance MS28 to maintain a list of nondominated points, from which the Model Reduction, Simulation and Optimization of new poll centers are chosen. The aim is to generate as a Load Change for a Molten Carbonate Fuel Cell many Pareto points as possible from the polling procedure itself, while keeping the whole framework general to ac- The ability of fast and save load changes is very important commodate other disseminating strategies. for stationary power plants powered by molten carbonate fuel cells. A hierachy of realistic and validated models ex- A. L. Custodio ist. They consist of upto 28 PDEs of parabolic and hyper- New University of Lisbon bolic type, some equations are degenerated. Part of the Department of Mathematics boundary conditions are given by a DAE. Numerical sim- [email protected] ulation and optimization results are presented. We compare especially some recently via model reduction devel- J. F. A. Madeira oped model variants with existing models. Technical University of Lisbon Armin Rund [email protected] University of Bayreuth, Department of Mathematics A. I. F. Vaz [email protected] University of Minho [email protected] Kurt Chudej University of Bayreuth, Lehrstuhl f. Ingenieurmathematik L. N. Vicente [email protected] University of Coimbra [email protected] Johanna Kerler University of Bayreuth MS29 [email protected] A Principled Stochastic Viewpoint on Derivative- 122 OP11 Abstracts

Free Optimization MS30 Randomized Dimensionality Reduction for Full- We consider numerical black-box optimization with little waveform Inversion assumptions on the underlying objective function. Fur- ther, we consider sampling from a distribution to obtain One of the major problems with full-waveform inversion new candidate solutions. Under mild assumptions, solv- is the requirement of solving large systems of discretized ing the original unknown optimization problem coincides PDE’s for each source (right-hand side). For 3-D prob- with optimizing a parametrized family of distributions of lems, this requirement is computationally prohibitive. To our choice. Following seminal works of Wierstra and Glas- address this fundamental issue, we propose a random- machers, we can now derive a gradient descend on the ized dimensionality-reduction strategy motivated by recent distribution manifold in a derivative-free problem context. developments in stochastic optimization and compressive For multivariate normal distributions this leads to a sim- sensing. In this formulation, conventional Gauss-Newton plified instantiation of CMA-ES. iterations are replaced by dimensionality-reduced sparse recovery problems with randomized source encodings. Nikolaus Hansen INRIA-Saclay, Université Paris-Sud, France Felix J. Herrmann [email protected] Seismic Laboratory for Imaging and Modeling The University of British Columbia [email protected] MS29 Derivative-Free methods for Mixed-Integer Opti- Tristan van Leeuwen, Aleksandr Aravkin, Xiang Li mization Problems the University of British Columbia We consider the problem of minimizing a continuously dif- [email protected], [email protected], ferentiable function of several variables where some of the [email protected] variables are restricted to take integer values. We assume that the first order derivatives of the objective function MS30 can be neither calculated nor approximated explicitly. We propose an algorithm convergent to points satisfying suit- Stochastic Optimization Framework for Design of able stationarity conditions. Integer variables are tackled Proper Orthogonal Decomposition Bases by a local search-type approach. Numerical results on a Numerical solution of large-scale Partial Differential Equa- difficult real application are presented and sustain the pro- tions (PDEs) is challenging from various aspects. The posed method. Proper Orthogonal Decomposition (POD) method has Stefano Lucidi been commonly employed for projection of the solution University of Rome into a lower dimensional subspace. Despite the popular- [email protected] ity of the approach, its utility was hitherto limited due to the specificity of the POD basis to the model parameters and the corresponding right-hand-side it has been obtained Giampaolo Liuzzi from. In this study we propose a framework for the design CNR - IASI of POD bases. The design problem is formulated as a non- [email protected] linear optimization problem with PDEs and reduced order PDE constraints. In order to account for model space vari- Francesco Rinaldi ability with respect to the model and the right-hand-side, University of Rome we resort to a Stochastic Sampling Average (SSA) formu- [email protected] lation. Since the design process can be computationally intensive, we accelerate the procedure by the incorporation of stochastic trace estimators. Numerical studies, ad- MS29 dressing the solution of large-scale problems, indicate the Optimization With Some Derivatives superiority of the designed bases upon their conventional counterparts. What is the value of knowing some partial derivatives in simulation-based optimization? We attempt an answer Lior Horesh through our experience extracting additional structure on Business Analytics and Mathematical Sciences problems consisting of both blackbox and algebraic com- IBM TJ Watson Research Center ponents. These problems include knowing derivatives: of [email protected] some residuals in nonlinear least squares problems, of some nonlinear constraints, and with respect to a subset of the Eldad Haber variables. In each case we use quadratic surrogates to Department of Mathematics model both the blackbox and algebraic components. The University of British Columbia Stefan Wild [email protected] Argonne National Laboratory [email protected] Marta D’Elia MathCS, Emory University Jorge J. Moré [email protected] Argonne National Laboratory Div of Math & Computer Science MS30 [email protected] 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 techniques MS31 in parameter estimation for partial diﬀerential equations. Geometric Duality for Convex Vector Optimization The comparison includes both full-space and reduced-space Problems formulations and algorithms based on these approaches. In order to evaluate their performance, we provide a series of Recently, a geometric duality theory for linear vector op- numerical experiments related to a data reduction tech- timization problems was developed. That theory provides nique based on compressed sensing. an inclusion-reversing one-to-one correspondence between ’optimal’ faces of the image sets of the primal and the dual Denis Ridzal, Joseph Young problem. We will extend this theory to the more general Sandia National Laboratories case of convex vector optimization problems. [email protected], [email protected] Frank Heyde Institute of Mathematics MS30 University of Halle-Wittenberg Compressed Sensing in a Finite Product of Hilbert [email protected] Spaces

We present an extension of the theory of compressed sens- MS31 ing to finite products of Hilbert spaces. This enables the Algorithms for Linear Vector Optimization Prob- use of compressed sensing in domains such as Sobolov lems spaces which are the natural setting for partial differential equations (PDEs). Using this extension, we reduce In 1998, Benson proposed a very efficient method to solve the cost of solving systems of PDEs where each equation linear vector optimization problems, called outer approx- uses identical differential operators. Our result allows a imation method. The idea is to construct the minimal reduction in the computational cost of an important class points in the outcome space. Geometric duality for mul- of parameter estimation problems. tiobjective linear programming can be used to derive a dual variant of Benson’s outer approximation algorithm. Joseph Young,DenisRidzal Moreover, this duality theory can be used to obtain inner Sandia National Laboratories approximations. We propose an extension of Benson’s al- [email protected], [email protected] gorithm as well as its dual variant which applies also to problems with an unbounded feasible set. This means that arbitrary linear vector optimization problems with the or- MS31 dinary ordering cone and having at least one minimal ver- Optimization over a Pareto Set in Multi-Objective tex can be solved. Control Problems Andreas Loehne My talk deals with the problem of optimizing a nonsmooth Institute of Mathematics real valued function over the efficient (Pareto) control pro- University of Halle-Wittenberg cesses set associated to a multi-objective control problem [email protected] (grand coalition of a multi-player cooperative differential game). This problem may be considered as an attempt to help a decision maker in his choice of an efficient control MS32 process, because the efficient set is often very large (infi- On Hilbert’s Theorem about Nonnegative Polyno- nite) and not explicitly described. mials in Two Variables

Henri Bonnel In 1893 Hilbert showed that for every nonnegative bivari- ERIM, University of New Caledonia ate polynomial p of degree 2d there exists a nonnegative [email protected] bivariate polynomial q of degree 2d − 4 such that pq is a sum of squares. Hilbert’s proof is not well understood, and there are no modern expositions of it. As a consequence, MS31 the result itself is largely forgotten. I will explain a new Optimality Conditions for Vector Optimization proof of this result. Problems with Variable Ordering Structures Greg Blekherman Motivated by some recent applications e.g. in medical im- University of California, San Diego age registration we discuss vector optimization problems [email protected] with a variable ordering structure. This structure is assumed to be given by a cone-valued map which associates to each element of the space a cone of preferred or domi- MS32 nated directions. For the case when the values of the cone- Moment Matrices and the Tensor Decomposition valued map are Bishop-Phelps cones we obtain for the ﬁrst Problem time scalarizations and based on that Fermat and Lagrange multiplier rule. In this talk, we will describe some connections between tensor decomposition, algebraic duality and moment matrices. Gabriele Eichfelder We will show how exploiting the structure of these matri- Department of Mathematics ces can help solving the decomposition problem for general University of Erlangen-Nuremberg or symmetric tensors. This approach will be illustrated by [email protected] some applications in geometric modelling.

Truong Xuan Duc Ha Bernard Mourrain Institute of Mathematics of Hanoi INRIA Sophia Antipolis [email protected] [email protected] 124 OP11 Abstracts

MS32 Israel Inverse Moment Problem for n-dimensional Poly- [email protected] topes The inverse moment problem asks to find the measure given MS33 (some of) its moments. It is well-studied in the case of Robust Optimization Made Easy with ROME the measures supported on a plane polygon, and can be solved exactly for convex polygons. In bigger dimensions, We introduce ROME, a MATLAB-based algebraic mod- however, it was not known how to solve it exactly even in eling toolbox for modeling a class of robust optimization the case of uniform measures supported on simple convex problems. ROME serves as an intermediate layer between polytopes, and all the known approximate methods relied the modeler and optimization solver engines, allowing mod- on slicing the unknown body into a large number of 2- elers to express robust optimization problems in a math- dimensional cylinders. We present a novel approach that ematically meaningful way. Using modeling examples, we produces exact answers, as well as is it capable of approxi- discusshowROMEcanbeusedtomodelandanalyzero- mate solving. Along the way we show that O(N) moments, bust optimization problems. ROME is freely distributed for N being the number of vertices of the convex polytope, for academic use from www.robustopt.com. suffice to reconstruct it. Joint work with N. Gravin, J. Lasserre, and S. Robins Joel Goh Stanford University Dmitrii Pasechnik [email protected] Nanyang Technological University [email protected] Melvyn Sim NUS Business School [email protected] MS32 Using Sums of Squares and Semidefinite Program- ming to Approximate Amoebas MS33 Robust Optimization of Nonlinear Constrained Dy- Amoebas are the logarithmic images of algebraic vari- namic Systems eties. We present new techniques for tackling computational problems on amoebas (such as the membership prob- We present a technique to solve robust optimal control lem) based on sums of sums of squares techniques and problems for nonlinear dynamic systems in a conservative semidefinite programming. Our method yields polynomial approximation. Here, the nonlinear dynamic system is af- identities as certificates of non-containedness of a point in fected by an uncertainty whose L-infinity norm is known an amoeba. As main theoretical result, we establish some to be bounded. In a second part of the talk, we address degree bounds on the polynomial certificates. Moreover, the discretized problem, a min-max nonlinear program, by we provide some actual computations of amoebas based on a novel variant of SQP type methods, sequential bi-level the sums of squares approach. (Joint work with Timo de quadratic programming. Both techniques are illustrated Wolff.) by applying them to numerical examples. Thorsten Theobald Boris Houska J.W. Goethe-Universität KU Leuven Frankfurt am Main, Germany [email protected] [email protected] Moritz Diehl K.U.Leuven MS33 [email protected] Immunizing Conic Quadratic Optimization Prob- lems Against Implemention Errors MS33 We show that the robust counterpart of a convex quadratic Distributionally Robust Joint Chance Constraints constraint with ellipsoidal implementation error is equiva- with Second-Order Moment Information lent to a system of conic quadratic constraints. To prove this result we first derive a sharper result for the S-lemma We develop tractable SDP-based approximations for dis- in case the two matrices involved are simultaneously di- tributionally robust chance constraints, assuming that only agonizable. This extension of the S-lemma may also be the first- and second-order moments and the support of the useful for other purposes. We also extend the results to uncertain parameters are given. We prove that robust in- the case of conic quadratic constraints with implementa- dividual chance constraints are equivalent to Worst-Case tion error. Several applications are discussed, e.g., design Conditional Value-at-Risk constraints. We also develop centering, robust linear programming with both parameter a conservative approximation for joint chance constraints, uncertainty and implementation error, and quadratic deci- whose tightness depends on a set of scaling parameters. sion rules for the adjustable robust optimization problem. We show that this approximation becomes exact when the scaling parameters are chosen optimally. Dick Den Hertog Steve Zymler, Daniel Kuhn,BercRustem Tilburg University Imperial College London Faculty of Economics and Business Administration [email protected], [email protected], [email protected] [email protected]

Aharon Ben-Tal Technion - Israel Institue of Technology OP11 Abstracts 125

MS34 vex Quadratic Programs with Cone Constraints Building a Completely Positive Factorization We present a generalization of the well-known result stating Using a bordering approach, and building upon an already that any non-convex quadratic problem over the nonneg- known factorization of a principal block, we establish suffi- ative orthant with some additional linear and binary con- cient conditions under which we can extend this factoriza- straints can be rewritten as linear problem over the cone of tion to the full matrix. Simulations show that the approach completely positive matrices. The generalization is done by is promising also in higher dimensions, provided there is no replacing the nonnegative orthant with an arbitrary closed gap in the cp-rank. Also, a construction of instances with convex cone. This set-semidefinite representation result guaranteed high cp-rank is presented. implies new semidefinite lower bounds for quadratic problems over several Bishop-Phelps cones, presented in the Immanuel Bomze talk University of Vienna [email protected] Janez Povh Faculty of Information Studies in Novo Mesto janez.povh@fis.unm.si MS34 Checking if a Sparse Matrix is Completely Positive Gabriele Eichfelder Department of Mathematics The completely positive cone is useful in optimization as it University of Erlangen-Nuremberg can be used to create convex formulations of NP-complete [email protected] problems. In this talk we discuss the problem of checking if a sparse matrix is completely positive and finding its cp- rank when it is. We present a linear time algorithm for MS35 preprocessing a matrix to reduce the problem. For spe- Robust Independence Systems cial types of matrices, for example acyclic matrices, this algorithm in fact solves the problem. This talk discusses the robustness for independence systems, which is a natural generalization of the greedy prop- Peter Dickinson erty of matroids. An independent set X is called α-robust University of Groningen if for any k, it includes an α-approximation of the maxi- [email protected] mum k-independent set (i.e., an independent set with size at most k). We show every independence system F has a F F MS34 1/ μ( )-robust independent set, where μ( ) denotes the exchangeability of F. Our result provides better bounds A Copositive Approach for Perfect Graphs for various independence systems.

If equality between the chromatic number and the click Naonori Kakimura, Kazuhisa Makino number of a graph holds, and if the same is true for any University of Tokyo of its induced subgraphs, the graph is called perfect. Re- [email protected], cently, in their celebrated paper ”The strong perfect graph [email protected] theorem”, Chudnovsky, Robertson, Seymour and Thomas proved that a graph is perfect if and only if it does not contain an odd hole or odd antihole (with at least 5 nodes) as MS35 an induced subgraph. Shortly after, Chudnovsky, Corne- A Primal-Dual Algorithm for Lattice Polyhedra jouls, Liu, Seymour and Vuskovic proved that recognition of perfect graphs can also be done in polynomial time. Hoffman and Schwartz developed 1978 the Lattice Poly- If a graph is perfect, its chromatic number can be deter- hedron model and proved that it is totally dual inte- mined by a polynomial time algorithm. It was proven by gral (TDI), and so has integral optimal solutions. The Grtschel, Lovsz and Schrijver in late 80’s, and their algo- model generalizes many important combinatorial optimiza- rithm is based on semidefinite programming. Nevertheless, tion problems, but has lacked a combinatorial algorithm. one of the most intriguing open questions related to perfect We developed the first combinatorial algorithm for this graphs is the design of pure combinatorial polynomial time problem, based on the Primal-Dual Algorithm framework. algorithm for determining their chromatic numbers. We The heart of our algorithm is an efficient routine that uses present some copositive formulations for the clique num- an oracle to solve a restricted abstract cut packing/shortest ber and the chromatic number of a graph, and study their path subproblem. This plus a standard scaling technique connections for the class of perfect graphs. We show how yields a polynomial combinatorial algorithm. The talk will such an approach can link the result of Grtschel, Lovsz and cover an introduction to the Lattice Polyhedron model, as Schrijver with pure combinatorial approaches. Still, one of well as a description of this primal-dual algorithm. the most intriguing questions of combinatorial optimization is the existence of pure combinatorial algorithm. We Britta Peis will revisit some known mathematical programming formu- T. U. Berlin lations for the stable set number [email protected]

Nebojsa Gvozdenovic S. Thomas McCormick University of Novi Sad Sauder School of Business, Vancouver, Canada [email protected] [email protected]

MS34 MS35 On the Set-Semideﬁnite Representation of Noncon- Principal Partition and the Matroid Secretary 126 OP11 Abstracts

Problem over a mixed integer polyhedral set. We solve the resulting problems using an outer approximation approach, where The goal in the Random Assignment Model of Matroid Sec- we apply an SQP-based algorithm to solve the nonlinear retary Problem is to select a maximum weight independent subproblems. Computational results for large-scale portfo- set of elements that arrive online in a random order. The lio optimization problems are presented both for the con- weights are chosen by an adversary but are assigned ran- tinuous as well as for the mixed integer setting. domly to the elements from the matroid ground set. By exploiting the principal partition of a matroid and its de- Sarah Drewes composition into uniformly dense minors we give the first Technische Universität Darmstadt, Department of constant factor competitive algorithm for this problem. Mathematics University of California - Berkeley Jose A. Soto [email protected] MIT [email protected] Sebastian Pokutta Massachusetts Institute of Technology MS35 [email protected] Generic Rigidity Matroids with Dilworth Trunca- tions MS36 We prove that the linear matroid that defines generic rigid- Optimistic MILP Approximations of Non-Linear ity of d-dimensional body-rod-bar frameworks (i.e., struc- Optimization Problems tures consisting of disjoint bodies and rods linked by bars) d+1 We present a new piecewise-affine approximation of non- can be obtained from the union of 2 graphic matroids linear optimization problems that can be seen as a general- by applying variants of the Dilworth truncation nr times, ization of the classical Union Jack triangulation. Roughly where nr denotes the number of rods. This leads to an speaking, it is a generalization because it leaves more de- alternative proof of Tay’s combinatorial characterizations grees of freedom to define any point as a convex combina- of generic rigidity of rod-bar frameworks and that of iden- tion of the samples. As an example, for the classical case of tified body-hinge frameworks. approximating a function of two variables, a convex combination of four points instead of only three is used. Be- Shin-ichi Tanigawa cause a plane is defined by only three independent points, Kyoto University the approximation obtained by triangulation is uniquely [email protected] determined, while different approximations are possible in our case. If embedded in a Mixed-Integer Linear Program- MS36 ming (MILP) model the choice among those alternatives is (optimistically) guided by the objective function. An ad- An Outer-Inner Approximation for Separable vantage of the new approximation within an MILP is that MINLP it requires a significant smaller number of additional binary We study Mixed Integer Nonlinear programs, where all variables and the logarithmic representation of these vari- nonlinear functions are convex and separable. One of the ables recently proposed by Vielma and Nemhauser can be most efficient approaches to solve Mixed Integer Nonlin- applied. We show theoretical and computational evidence ear programs is Outer Approximation. We show that even of the quality of the approximation and its impact within when all nonlinear function are separable Outer Approxi- MILP models. mation based algorithms can require the generation of an Andrea Lodi, Claudia D’Ambrosio exponential number of iterations to converge. We propose a University of Bologna cure that exploits the separability of the functions. We also DEIS combine the modified outer approximation with an inner [email protected], [email protected] approximation scheme in order to obtain good feasible solution. We test the practical effectiveness of our approach on an application in the telecommunications industry. Silvano Martello DEIS, University of Bologna Pierre Bonami [email protected] Laboratoire d’Informatique Fondamentale de Marseille [email protected] Riccardo Rovatti DEIS and ARCES, University of Bologna Hassan Hijazi [email protected] LIX, Ecole Polytechnique, Palaiseau, France [email protected] MS36 Global Optimization of Equilibirum Constrained Adam Ouorou Networks France Telecom R&D-Orange Labs [email protected] Network flows are generally governed by an equilibrium principle such as Kirchoffs Laws in electrical networks, Wardrop Principle in transportation networks and Laws MS36 of Static Equilibrium in structural networks. All of above Maximizing Expected Utility in the Presence of problem classes can be reduced to networks with nonlin- Discrete Decisions ear resistances. Earlier formulations cast the problem as a non-convex and non-smooth MINLP with no guarantee of We consider the problem of maximizing expected logarith- global optimality. We present a novel convex MINLP for- mic utility in conjunction with a linear objective function mulation and describe an algorithm based on linearizations OP11 Abstracts 127

for the efficient solution. We also describe a new projected tions cited above). nonlinear cut that can be generalized to the class of Con- vex Disjunctive Programs. Effectiveness of the perspective Mikhail V. Solodov cut for this class of problems will also be explored. Re- Inst de Math Pura e Applicada sults demonstrating the effectiveness of the approach on [email protected] applications from literature will be presented. Damian Fernandez Arvind Raghunathan FaMAF, Univ. de Cordoba United Technologies Research Center Argentina [email protected] [email protected]

MS37 MS37 Practical Algorithmic Strategies in Augmented La- Matrix-free Nonlinear Programming for Dynamic grangians Optimization Practical strategies for improving the eﬀectiveness of Aug- We investigate dynamic optimization problems that appear mented Lagrangian methods will be discussed in the in nonlinear model predictive control. Such problems can present work. The outer-trust region strategy for deal- be represented as parametric variational inequality probing with the so called greediness phenomenon will be de- lems. Aiming for real-time performance in a resource- scribed. A nonmonotone scheme for increasing the penalty limited environment, we propose a method that solves in- parameter will also be discussed. Theoretical results will exactly a quadratic program per step and prove that it sta- be presented and numerical evidences of the usefulness of bly tracks the optimal manifold. We demonstrate how the the suggested strategies will be analysed. approach can be implemented in an iterative matrix-free framework by using an augmented Lagrangian approach. Ernesto G. Birgin Department of Computer Science - IME Victor Zavala University of So Paulo Argonne National Laboratory [email protected] [email protected]

MS37 Mihai Anitescu Argonne National Laboratory Augmented Lagrangian Filter Methods Mathematics and Computer Science Division We introduce a two-phase method for large-scale nonlinear [email protected] optimization. In the first phase, projected-gradient iterations approximately minimize the augmented Lagrangian MS38 to estimate the optimal active set. In the second phase, we solve an equality-constrained QP. An augmented La- Numerical Methods for Model Discrimination in grangian filter determines the accuracy of the augmented Chemistry and Biosciences Lagrangian minimization and promotes global conver- If two or more model candidates are proposed to describe gence. Our algorithm is designed for large-scale optimiza- the same process and information available does not allow tion, and we present promising numerical results. to discriminate between the candidates, new experiments Sven Leyffer must be designed to reject models by lack-of-fit test. Math- Argonne National Laboratory ematically this leads to highly structured, complex, mul- leyff[email protected] tiple experiments, multiple models optimal control problems. Special emphasis is placed on robustification of optimal designs against uncertainties in model parameters. MS37 New numerical methods and applications from chemistry Local Convergence of Exact and Inexact Aug- and biosciences will be discussed. mented Lagrangian Methods under the Second- Thorsten Ante, Ekaterina Kostina, Gregor Kriwet order Sufficiency Condition Fachbereich Mathematik und Informatik We establish local convergence and rate of convergence of Philipps-Universitaet Marburg the classical augmented Lagrangian algorithm (also known [email protected], as the method of multipliers) under the sole assumption [email protected], [email protected] that the dual starting point is close to a multiplier satisfying the second-order sufficient optimality condition. In par- MS38 ticular, no constraint qualifications of any kind are needed. Previous literature on the subject required the linear inde- Challenges of Parameter Identification for Nonlin- pendence constraint qualification and, in addition, either ear Biological and Chemical Systems the strict complementarity assumption or the stronger ver- Mathematical models ensuring a highly predictive power sion of second-order sufficiency. For sufficiently large values are of inestimable value in systems biology. Their applica- of the penalty parameters we prove primal-dual Q-linear tion ranges from investigations of basic processes in living convergence rate, which becomes superlinear if the param- organisms up to model based drug design in the field of eters are allowed to go to infinity. Both exact and inexact pharmacology. For this purpose simulation results have to solutions of subproblems are considered. In the exact case, be in consistency with the real process, i.e., suitable model we further show that the primal convergence rate is of the parameters have to be identified minimizing the difference same Q-order as the primal-dual rate. Previous assertions between the model outcome and measurement data. In for the primal sequence all had to do with the the weaker this work, graph based methods are used to figure out R-rate of convergence (and required the stronger assump- 128 OP11 Abstracts

if conditions of parameter identifiability are fulfilled. In approach. combination with network centralities, the structural representation of the underlying mathematical model provides Roland Herzog a first guess of informative output configurations. As at Chemnitz University of Technology least the most influential parameters should be identifiable [email protected] and to reduce the complexity of the parameter identification process further a parameter ranking is done by Sobol’ Ekkehard W. Sachs indices. The calculation of these indices goes along with University of Trier a highly computational effort, hence monomial cubature Virginia Tech rules are used as an efficient approach of numerical inte- [email protected] gration. In addition, a joint application of the previously introduced methods enables an online model selection process, i.e., operation conditions can be derived that make MS39 previously undistinguishable model candidates distinguish- All-at-once Solution of Time-dependent PDE- able. The feature of an online framework is quite attractive constrained Optimization Problems as it avoids the need for additional time consuming experiments. All methods are demonstrated for a well known Time-dependent partial differential equations (PDEs) play motif in signaling pathways, the MAP kinase cascade. an important role in applied mathematics and many other areas of science. One-shot methods try to compute the so- Michael Mangold lution to these problems in a single iteration that solves Max-Planck-Institut für Dynamik komplexer technischer for all time-steps at the same time. In this talk, we look System at one-shot approaches for the optimal control of time- Magdeburg, Germany dependent PDEs and focus on the fast solution of these [email protected] problems. The use of Krylov subspace solvers together with an efficient preconditioner allows for minimal storage Rene Schenkendorf requirements. We solve only approximate time-evolutions Max-Planck-Institut fuer Dynamik komplexer technischer for both forward and adjoint problem and compute accu- Systeme, Magdeburg, Germany rate solutions of a given control problem only at conver- [email protected] gence of the overall Krylov subspace iteration. We show that our approach can give competitive results for a variety of problem formulations. MS38 Robust Optimal Experimental Design for Model Martin Stoll discrimination of Dynamic Biochemical Systems Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Finding suitable models of dynamic biochemical systems is Syste an important task in the biosciences. On the one hand a [email protected] correct model can explain the underlying mechanisms on the other hand one can use the model to predict the be- Andrew J. Wathen havior of a biological system under various circumstances. Oxford University We present a computational framework to compute robust Numerical Analysis Group optimal experimental designs for the purpose of model dis- [email protected] crimination. Dominik Skanda MS39 Department of Applied Mathematics Preconditioning for An Option Pricing Problem University of Freiburg, Germany [email protected] The pricing of European option using Merton’s model leads to a partial integro-differential equation (PIDE). The nu- Dirk Lebiedz merical solution involves the solution of linear systems with University of Freiburg dense coefficient matrices. We use a preconditioned con- Center for Systems Biology jugate gradient method combined with fast Fourier trans- [email protected] form. The choice of the preconditioners is studied thor- oughly, including estimates for the spectrum and mesh independence of the number of iterates required. The results MS39 are extended to relevant optimization problem and further Preconditioned Conjugate Gradient Method for discussed in such a context. Optimal Control Problems with Control and State Constraints Xuancan Ye FB IV - Department of Mathematics We consider saddle-point problems arising as linearized op- University of Trier timality conditions in optimal control problems. The effi- [email protected] cient solution of such systems is a core ingredient in second- order optimization algorithms. In the spirit of Bramble Ekkehard W. Sachs and Pasciak, the preconditioned systems can be turned into University of Trier symmetric and positive definite ones with respect to a suit- Virginia Tech able scalar product. We focus on the solution of problems [email protected] with control and state constraints and provide numerical examples in 2D and 3D to illustrate the viability of our MS39 Robust Preconditioners for Distributed Optimal OP11 Abstracts 129

Control of the Stokes Equations Denmark [email protected] In this talk an optimal control problem for steady state Stokes flow with distributed control is considered. The Pietro Simone Oliveto optimal control problem involves a regularization param- University of Birmingham eter, say α, in the cost functional. For solving the dis- [email protected] cretized optimality system, we will present preconditioned Krylov subspace methods whose convergence rate is uniformly bounded in α. MS40 Walter Zulehner Some Applications of Evolutionary Computation University of Linz, Austria This talk introduces some applications of evolutionary al- [email protected] gorithms, including data-driven modelling in astrophysics and materials engineering, route optimisation for salting MS40 trucks in winter, multi-objective design of digital filters, software testing resource allocation, redundancy allocation Convergence Properties of Evolution Strategies in maximising system reliability, etc. The primary aim Evolution strategies (ESs) are stochastic optimization algo- of this talk is to illustrate innovative applications of vari- rithms for numerical optimization. In each iteration of an ous randomised search heuristics, rather than trying to be ES, internal parameters are updated using the ranking of comprehensive. candidate solutions and not their intrinsic objective func- Xin Yao tion value. In this talk, we review linear convergence re- University of Birmingham sults for evolution strategies and discuss the consequences [email protected] of the rank-based update in terms of lower bounds for convergence rates and invariance classes for the set of functions where linear convergence holds. MS42 Anne Auger The Infinite Push: A New Support Vector Ranking INRIA Saclay Algorithm that Directly Optimizes Accuracy at the [email protected] Absolute Top of the List I will describe a new ranking algorithm called the ‘Infi- MS40 nite Push’ that directly optimizes ranking accuracy at the absolute top of the list. The algorithm is a support vec- Stochastic Second-Order Method for Function- tor style algorithm, but due to the different objective, it ValueFreeNumericalOptimization no longer leads to a quadratic programming problem. In- We review the counterpart of Quasi-Newton methods in stead, the dual optimization problem involves l1,∞ con- evolutionary computation: the covariance matrix adapta- straints; we solve this using an efficient gradient projection tion evolution strategy, CMA-ES. The CMA-ES adapts a method. Experiments on real-world data sets confirm the second-order model of the underlying objective function. algorithm’s focus on accuracy at the absolute top of the On convex-quadratic functions, the resulting covariance list. matrix resembles the inverse Hessian matrix. Surprisingly, Shivani Agarwal this can be accomplished derivative- and function-value Indian Institute of Science free.TheCMA-ESrevealsthesameinvarianceproper- [email protected] ties as the Nelder-Mead method, works reliably not only in low dimension and is surprisingly efficient also on convex and non-convex, highly ill-conditioned problems. MS42 Nikolaus Hansen A Graph Theoretical Approach to Preference INRIA-Saclay, Université Paris-Sud, France Based Ranking: Survey of Recent Results [email protected] I will survey recent results for preference based ranking from a graph theoretical perspective, where the problem MS40 is known as ”Minimum Feedback Arc-Set”. The following results will be highlighted: A simple 3-approximation using Theory of Randomized Search Heuristics in Com- QuickSort, a PTAS by Kenyon and Schudy and a more binatorial Optimization recent sub-linear version of the PTAS. Special attention We analyze the runtime and approximation quality of will be paid to the important Rank Aggregation case, in randomized search heuristics when solving combinatorial which the input is a convex combination of permutations. optimization problems. Our studies treat simple local- Nir Ailon search algorithms and simulated annealing as well as more Technion Israel Institute of Technology complex population-based evolutionary algorithms. The [email protected] combinatorial optimization problems discussed include the maximum matching problem, the partition problem and the minimum spanning tree problem as an example where MS42 Simulated Annealing beats the Metropolis algorithm in Bayesian Ranking combinatorial optimization. Important concepts of the analyses will be sketched as well. I will present several large-scale applications of Bayesian ranking algorithms to various domains including (1) gamer Carsten Witt ranking on Xbox Live (”TrueSkill”), (2) professional chess Technical University of Denmark gamer ranking across their lifetime (”TrueSkill-through- 130 OP11 Abstracts

Time”), (3) research school ranking in the 2008 British cal. We present an efficient convex optimization-based al- Research Assessment Exercise, and (4) ranking of adver- gorithm we call Outlier Pursuit that recovers the exact tisements (adPredictor) on Microsoft’s search engine, bing. optimal low-dimensional subspace, and identifies the cor- The key challenge in all these domains is data sparsity per rupted points. We extend this to the partially observed entity - usually there are only O(log(n)) comparisons avail- setting, significantly extending matrix completion results able for O(n) entities. I will also present an information to the setting of corrupted rows or columns. theoretic viewpoint of ranking for evaluating the efficiency of Bayesian ranking algorithms. Constantine Caramanis The University of Texas at Austin Ralf Herbrich [email protected] Microsoft Research Cambridge [email protected] MS43 Robustness Models in Learning MS42 New Models and Methodologies for Group Deci- Robust optimization is a methodology traditionally applied sion Making, Rank Aggregation, Clustering and to handle measurement errors or uncertainty about future Data Mining data in a decision problem. As such, it has a natural place in machine learning applications. In fact, classical learn- The aggregate ranking problem is to obtain a ranking that ing models such as SVMs or penalized regression can be is fair and representative of the individual decision makers’ interpreted in terms of robustness models. This interpre- rankings. We argue here that using cardinal pairwise com- tation leads to new insights into important aspects such parisons provides several advantages over score-wise or or- as consistency and sparsity of solutions. Building on these dinal models. The aggregate group ranking problem is for- connections, we show that robust optimization ideas can malized as the separation model and separation-deviation lead to new, more performant learning models that take model and linked to the inverse equal paths problem. This into account data structure, such as those arising in text new approach is shown to have advantages over PageRank classification, where the data is often boolean or integer- and the principal eigenvector methods. valued. Robustness models can also be used in the context of a large-scale learning problem with dense data, based Dorit Hochbaum on the idea of thresholding and taking into account the Industrial Engineering and Operations Research resulting error when solving the learning problem. University of California, Berkeley [email protected] Laurent El Ghaoui EECS, U.C. Berkeley [email protected] MS43 An Efficient Algorithm for Variable Sparsity Ker- nel Learning MS43 Robust High-Dimensional Principal Component We present algorithms and applications for a particular Analysis class of mixed-norm regularization based Multiple Kernel Learning (MKL) formulations. The formulations assume We revisit one of the perhaps most widely used statistical that the given kernels are grouped and employ L1 norm techniques for dimensionality reduction: Principal Com- regularization for promoting sparsity within each group, ponent Analysis (PCA). In the standard setting, PCA is and Lp norm for promoting non-sparse combinations across computationally efficient, and statistically consistent, i.e., groups. Various sparsity levels in combining the kernels can as the number of samples goes to infinity, we are guaranteed be achieved by varying the grouping of kernels—hence we to recover the optimal low-dimensional subspace. On the name the formulations as Variable Sparsity Kernel Learn- other hand, PCA is well-known to be exceptionally brittle ing (VSKL) formulations. While previous attempts have a – even a single corrupted point can lead to arbitrarily bad non-convex formulation, here we present a convex formula- PCA output. We consider PCA in the high-dimensional tion which admits efficient Mirror-Descent (MD) based al- regime, where a constant fraction of the observations in gorithm, combined with block coordinate descent method. the data set are arbitrarily corrupted. We show that stan- Experimental results show that the VSKL formulations are dard techniques fail in this setting, and discuss some of the well-suited for multi-modal learning tasks like object cate- unique challenges (and also opportunities) that the high- gorization. Results also show that the MD based algorithm dimensional regime poses. For example, one of the (many) outperforms state-of-the-art MKL solvers in terms of com- confounding features of the high-dimensional regime, is putational efficiency. that the noise magnitude dwarfs the signal magnitude, i.e., SNR goes to zero. While in the classical regime, dimen- Aharon Ben-Tal sionality recovery would fail under these conditions, sharp Technion - Israel Institue of Technology concentration-of-measure phenomena in high dimensions Israel provide a way forward. Then, for the main part of the talk, [email protected] we propose a High-dimensional Robust Principal Compo- nent Analysis (HR-PCA) algorithm that is computationally tractable, robust to contaminated points, and easily MS43 kernelizable. The resulting subspace has a bounded devia- Robust PCA and Collaborative Filtering: Reject- tion from the desired one, for up to 50% corrupted points. ing Outliers, Identifying Manipulators No algorithm can possibly do better than that, and there is currently no known polynomial-time algorithm that can Principal Component Analysis is one of the most widely handle anything above 0%. Finally, unlike ordinary PCA used techniques for dimensionality reduction. Neverthe- algorithms, HR-PCA has perfect recovery in the limiting less, it is plagued by sensitivity to outliers; finding robust analogs, particularly for high-dimensional data, is criti- OP11 Abstracts 131

case where the proportion of corrupted points goes to zero. University of Toulouse France Shie Mannor [email protected] Electrical Engineering Technion [email protected] MS44 Accelerated Projection Methods for Semidefinite Programs MS44 Copositivity and Constrained Fractional Quadratic Accelerated projection methods are particularly suitable Problems for optimization problems over the intersection of the semidefinite cone and the nonnegative cone or other poly- Completely Positive (CpPP) and Copositive Program- hedral cones of sparse structure such as triangle inequali- ming (CoP) formulations for the Constrained Fractional ties. We present a simple algorithm and numerical results Quadratic Problem (CFQP) and Standard Fractional for the Lovasz-Schrijver θ-number of graphs with up to Quadratic Problem (StFQP) are introduced. Dual and 1000 vertices. Primal attainability are discussed. Semidefinite Program- ming (SDP) formulations are proposed for finding good Florian Jarre lower bounds to these fractional programs. A global opti- Mathematisches Institut mization branch-and-bound approach is proposed for the Universitaet Duesseldorf, Germany StFQP. Applications of the CFQP and StFQP, related with [email protected] the correction of nfeasible linear systems and eigenvalue complementarity problems are also discussed. Thomas Davi Universitaet Duesseldorf, Germany Paula Amaral Mathematisches Institut Universidade Nova de Lisboa [email protected] Portugal [email protected] MS45 Immanuel Bomze Dynamic Markets as Differential Variational In- University of Vienna equalities [email protected] We investigate the effects of the physical layer of the energy Joaquim Judice infrastructure on the behavior of energy markets. We use Universidade de Coimbra differential variational inequalities as a flexible framework Portugal in which to describe both the market and physical lay- [email protected] ers. We investigate the effects of the various market design strategies and on the overall stability of the closed-loop system. We discuss the computational cost of the strategies of MS44 decision-makers and approximations that make them suit- Some New Results in Copositive Programming able for real-time environments. We will present some new results concerning the cones of Mihai Anitescu copositive and completely positive matrices which play an Argonne National Laboratory important role in quadratic and binary optimization. Mathematics and Computer Science Division [email protected] Mirjam Duer TU Darmstadt Victor Zavala [email protected] Argonne National Laboratory [email protected] MS44 Testing Copositivity with the Help of Difference- MS45 of-Convex Optimization Differential Variational Inequalities in Control

In this joint work with Mirjam Duer, we consider the prob- It is well-known that checking certain controllability prop- lem of minimizing an indefinite quadratic function over erties of very simple piecewise linear systems are undecid- the nonnegative orthant, or equivalently, the problem of able problems. This paper deals with the controllability deciding whether a symmetric matrix is copositive. We problem of a class of piecewise linear systems, known as formulate the problem as a difference-of-convex functions linear complementarity systems. By exploiting the under- (d.c.) problem. Using an appropriate conjugate duality, we lying structure and employing the results on the controlla- show that there is a one-to-one correspondence between bility of the so-called conewise linear systems, we present a their respective stationary points and minima. We then set of inequality type conditions as necessary and sufficient apply a subgradient algorithm to approximate those sta- conditions for controllability of linear complementarity sys- tionary points and obtain an efficient heuristic to verify tems. The presented conditions are of PopovBelevitch- non-copositivity of a matrix. Keywords: Copositive matri- Hautus type in nature. ces; difference-of-convex functions(d.c.); Legendre-Fenchel transforms; nonconvex duality; subgradient algorithms for Kanat Camlibel d.c.functions. University of Groningen Institute of Mathematics and Computer Science Jean-Baptiste Hiriart-Urruty [email protected] 132 OP11 Abstracts

MS45 zon optimal control problem in a receding horizon fashion. A Unified Numerical Scheme for Linear-Quadratic Consequently, the solution to this optimization problem Optimal Control Problems with Joint Control and has to be obtained within one sampling period of the con- State Constraints trol loop. But guaranteeing deterministic termination of iterative solution methods is a challenging problem in gen- We present a numerical scheme for the convex linear- eral. This talk focuses on certifying Nesterov’s fast gradient quadratic optimal control problem with mixed polyhedral method for constrained linear quadratic MPC and points state-control constraints. Unifying the technique of model out links between problem data and convergence speed. predictive control and a time-stepping method based on the differential variational inequality reformulation, the scheme Stefan Richter solves a sequence of finite-dimensional problems whose op- Institut für Automatik timal solutions are employed to construct a discrete-time ETH Zürich trajectory. Such a numerical trajectory is shown to con- [email protected] verge to an optimal trajectory of the continuous-time problem. Colin Jones, Manfred Morari Institut für Automatik Jong-Shi Pang ETH Zürich, Switzerland University of Illinois at Urbana-Champaign [email protected], [email protected] [email protected]

MS46 MS45 Fast Explicit Nonlinear MPC via Multiresolution Runge-Kutta Methods for Solving Differential Interpolet Approximation Variational Inequalities (DVIs) An algorithm for nonlinear explicit model predictive con- Runge-Kutta methods can be used for DVIs as they can be trol is introduced based on multiresolution function ap- used for differential inclusions (see Taubert (1976, 1981), proximation that returns a low complexity approximate Kastner-Maresch (1990), Dontchev & Lempio (1992)). receding horizon control law built on a hierarchy of sec- However, some issues arise in the DVI setting that com- ond order interpolets. Feasibility and stability guarantees plicate the proofs and results. Under conditions known to for the approximate control law are given using reachability imply uniqueness of solutions for the DVI, provided the analysis. A constructive algorithm is provided that results exact solution is smooth on a given time interval, it can in a control law that is built on a grid hierarchy that is fast be shown that the numerical solutions from certain Runge- to evaluate in real-time systems. Kutta methods have the appropriate orders of convergence. Included in these methods is the Radau IIA family of meth- Sean Summers, Davide Raimondo, Colin Jones, John ods which can give arbitrarily high order of convergence. Lygeros, Manfred Morari Institut für Automatik ETH Zürich, Switzerland David E. Stewart [email protected], University of Iowa [email protected], [email protected], Department of Mathematics [email protected], [email protected] [email protected]

MS46 MS46 Multilevel Iteration Schemes for Nonlinear Model Fast Mixed-integer Model-predictive Control Predictive Control

We present work on nonlinear model predictive control Although nonlinear model predictive control has seen many problems. In this problem class, some control functions theoretical and computational advances, the application to such as gear choices may only take values from a discrete systems requiring fast feedback is still a major computa- set.BasedonanOuterConvexification,onBock’sdirect tional challenge. In this contribution, we investigate new multiple shooting method, and on real-time iterations by multi-level iteration schemes, which distribute the compu- Diehl, Bock, and Schlöder we present a new mixed-integer tations occurring in SQP iterations among up to four in- real time iteration scheme and discuss theoretical and al- dependent levels, ranging from fast feedback on the lowest gorithmic aspects. level, where small QPs are solved very quickly, to complete derivative information generation on the topmost level. We Christian Kirches give details on the implementation and we apply the multi- Interdisciplinary Center for Scientific Computing level iteration schemes to some test problems. University of Heidelberg, Germany [email protected] Leonard Wirsching Interdisciplinary Center for Scientific Computing (IWR) Sebastian Sager Heidelberg University Interdisciplinary Center for Scientific Computing [email protected] [email protected] Hans Georg Bock IWR, University of Heidelberg MS46 [email protected] Computational Complexity Certificates for MPC Based on the Fast Gradient Method Johannes Schloeder MPC requires the solution of a constrained finite hori- IWR, University of Heidelberg, Germany [email protected] OP11 Abstracts 133

MS47 some of the structure detection problems on the graph On Convergence in Mixed Integer Programming theoretic side, formulate optimization problems for finding ”best” structures, and discuss their usefulness for the We define the integral lattice-free closure L(P )ofaratio- mentioned decomposition algorithms. nal polyhedron P as the set obtained from P by adding all inequalities obtained from disjunctions associated with Marco Lübbecke, Martin Bergner integral lattice-free sets. We show that L(P ) is again a RWTH, Aachen University polyhedron, and that repeatedly taking the integral lattice- [email protected], martin.bergner@rwth- free closure of P gives its mixed integer hull after a finite aachen.de number of iterations. Alberto Del Pia MS48 ETH Network Design with a Set of Traffic Matrices [email protected] A crucial assumption in many network design problems is that we are given a single matrix of traffic demands MS47 (and that is known in advance). Unfortunately, in sev- Crooked Cross Cuts for Mixed Integer Programs eral applications, communication patterns among terminals change over time, and therefore we are given a set D We describe a family of asymmetric disjunctive cuts called of non-simultaneous traffic matrices. Still, we would like crooked cross cuts. These cuts subsume two dimensional to design a min-cost network that is able to support any lattice-free cuts and they give the convex hull of mixed- traffic matrix that is from D. In this paper, we discuss integer programs with two integer variables (and many strategies for approaching this problem when D is a finite constraints). We also present separation heuristics and set. We settle a few complexity questions, present some encouraging computational results on standard test sets. approximation based results, and in some cases give exact Joint work with Sanjeeb Dash, Santanu Dey and Juan- polynomial-time algorithms. Pablo Vielma. Gianpaolo Oriolo Oktay Gunluk Università di Tor Vergata IBM, Watson, New York [email protected] [email protected] Laura Sanita’ Ecole Polytechnique Federale de Lausanne MS47 laura.sanita@epfl.ch Intersection Cuts with Infinite Split Rank

We consider a mixed integer linear programs where m free Rico Zenklusen integer variables are expressed in terms of nonnegative con- EPFL Lausanne tinuous variables. When m = 2, Dey and Louveaux char- [email protected] acterized the intersection cuts that have infinite split rank. ≥ We show that, for any m 2, the split rank of an intersec- MS48 tion cut generated from a bounded convex set P is finite if and only if the integer points on the boundary of P satisfy Steiner Tree Approximation Via Iterative Random- a certain “2-hyperplane property’. ized Rounding Amitabh Basu The Steiner tree problem is one of the most fundamen- Dept. of Mathematics tal NP-hard problems: given a weighted undirected graph Universiity of California, Davis G=(V,E) and a subset of terminal nodes, find a minimum [email protected] weight tree spanning the terminals. In this talk, we introduce a directed LP relaxation and describe an approximation algorithm based on iterative randomized rounding of a Gerard Cornuejols fractional solution. We prove an approximation guarantee Tepper School of Business of 1.39 for the algorithm (improving over the previously Carnegie Mellon University best known factor of 1.55) and show that the mentioned [email protected] LP has an integrality gap of at most 1.55 (improving over the previously best known factor of 2). This is joint work Francois Margot with Jaroslaw Byrka, Fabrizio Grandoni and Laura Sanita. Carnegie Mellon University Tepper School of Business [email protected] Thomas Rothvoss EPF Lausanne jocelyne.blanc@epfl.ch MS48 Detecting Structures in Matrices MS48 Permuting matrices into particular structures, like double- Scheduling and Power Assignments in the Physical bordered block-diagonal or staircase forms is an area of Model for Wireless Networks interest in e.g., numerical linear algebra for preparing a matrix for parallel processing. The topic is also interest- In the interference scheduling problem, one is given a set of ing when it comes to applying decomposition algorithms in n communication requests each of which corresponds to a linear and integer programming. As there is a canonical re- sender and a receiver in a multipoint radio network. Each lationship between matrices and (hyper-)graphs, we study request must be assigned a power level and a color such 134 OP11 Abstracts

that signals in each color class can be transmitted simul- ETSI Ind y de Telecomm taneously. The feasibility of simultaneous communication [email protected] within a color class is defined in terms of the signal to interference plus noise ratio (SINR) that compares the strength Roland Herzog of a signal at a receiver to the sum of the strengths of Chemnitz University of Technology other signals. This is commonly referred to as the physical [email protected] model and is the established way of modeling interference in the engineering community. The objective is to mini- Gerd Wachsmuth mize the schedule length corresponding to the number of TU Chemnitz colors needed to schedule all requests. We study oblivious Fakultät für Mathematik powerassignmentsinwhichthepowervalueofarequest [email protected] only depends on the path loss between the sender and the receiver, e.g., in a linear fashion. At first, we present a measure of interference giving lower bounds for the schedule MS49 length with respect to linear and other power assignments. Bang Bang Control of Elliptic PDEs Based on this measure, we devise distributed scheduling algorithms for the linear power assignment achieving the In this talk we describe the use of variational approach in minimal schedule length up to small factors. In addition, order to discretize elliptic optimal control problems with we study a power assignment in which the signal strength bang-bang controls. We prove error estimates for the re- is set to the square root of the path loss. We show that sulting scheme and present a numerical example which sup- this power assignment leads to improved approximation ports our analytical findings. guarantees in two kinds of problem instances defined by directed and bidirectional communication request. Finally, Nikolaus von Daniels we study the limitations of oblivious power assignments by Universität Hamburg proving lower bounds for this class of algorithms. Fachbereich Mathematik [email protected] Berthold Vocking RWTH Aachen University Klaus Deckelnick [email protected] Otto-von-Guericke-University Magdeburg [email protected] MS49 On a Problem of Optimal Control of Magnetic Michael Hinze Fields Universität Hamburg Department Mathematik A problem of optimal magnetization is considered. It is [email protected] related to the time-optimal switching between magnetic fields and leads to the minimization of a tracking type functional subject to a system of parabolic equations of differ- MS49 ential algebraic type. We discuss the sensitivity analysis A Priori Error Analysis of the Petrov Galerkin and present 3D numerical results for a slightly simplified Crank Nicolson Scheme for Parabolic Optimal geometry. Control Problems Kristof Altmann In this talk, a finite element discretization of an optimal Technische Universitaet Berlin control problem governed by the heat equation is consid- Institut fuer Mathematik ered. The temporal discretization is based on a Petrov [email protected] Galerkin variant of the Crank Nicolson scheme, whereas the spatial discretization employs usual conforming finite Fredi Troeltzsch elements. With a suitable post-processing step, a discrete Techn. University of Berlin solution is obtained for which error estimates of optimal Department of Mathematics order are proven. A numerical result is presented for illus- [email protected] trating the theoretical findings. Boris Vexler, Dominik Meidner MS49 Technische Universitaet Muenchen Centre for Mathematical Sciences, M1 Error Estimates for an Optimal Control Problem [email protected], [email protected] with a Non Differentiable Cost Functional

In this talk, semilinear elliptic optimal control problems MS50 involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimal- SQP Methods for Large-scale NLP ity conditions are derived. A priori finite element error es- Recent advances in MINLP and the solution of NLPs with timates for piecewise constant discretizations for the con- differential equation constraints have revived interest in trol and piecewise linear discretizations of the state are methods that may be warm started from a good estimate shown. Error estimates for the variational discretization of a solution. In this context, we review some recent devel- of the problem, as introduced by Hinze (2005), are also opments in methods for large-scale convex and nonconvex obtained. Finally, numerical experiments confirm the con- quadratic programming and consider the use of these meth- vergence rates. ods in a sequential quadratic programming (SQP) method Eduardo Casas that exploits both first and second derivatives of the ob- Universidad de Cantabria OP11 Abstracts 135

jective and constraint functions.

Philip E. Gill, Elizabeth Wong Daniel Robinson University of California, San Diego Oxford University Department of Mathematics [email protected] [email protected], [email protected] Philip E. Gill University of California, San Diego MS50 Department of Mathematics Preconditioners for Matrix-free Interior Point [email protected] Method

A new variant of Interior Point Method (IPM) will be MS52 addressed which allows for a matrix-free implementation. Integer Optimization Methods for Ranking Prob- Preconditioner(s) suitable in this context will be presented lems in Machine Learning and their spectral properties will be analysed. The performance of the method will be illustrated by computational In supervised ranking, the goal is to optimize a ”rank results obtained for very large scale optimization problems. statistic,” which measures the quality of a ranked list. We This work is an extension of the paper available from: present novel mixed integer programming (MIP) formula- http://www.maths.ed.ac.uk/~gondzio/reports/mtxFree.htmltions. for a wide variety of supervised ranking tasks. Other ranking methods use convex functions to approximate rank statistics in order to accommodate extremely large prob- Jacek Gondzio lems. In contrast, our MIP approach provides exact mod- The University of Edinburgh, United Kingdom eling. We report computational results that demonstrate [email protected] signiﬁcant advantages for MIP methods over current state- of-the-art.

MS50 Dimitris Bertsimas, Allison Chang CQP: a Fortran 90 Module for Large-Scale Convex Massachusetts Insitute of Technology Quadratic Programming [email protected], [email protected] We describe the design of a new software package CQP for large-scale convex quadratic programming. The method Cynthia Rudin is based on high-order Taylor and Puiseux approximation Massachusetts Institute of Technology to a variety of infeasible arcs connecting the current iter- [email protected] ate to a better target point. Possible arcs include those by Zhang and by Zhou and Sun based on work by Stoer, MS52 Mizuno, Potra and others. The resulting algorithm is provably both globally and polynomially convergent at an ul- Learning to Rank with a Preference Function timately high-order (depending on the series used) in both We discuss novel algorithmic solutions to the problem of non-degenerate and degenerate cases. We will illustrate a learning to rank in the preference-based setting. This number of algorithmic options on the CUTEr QP test set. formulation of the ranking problem is important since it CQP is available as part of the fortran 90 library GALA- closely models that of search engines. Its crucial advan- HAD. tage is that it does not require the learning algorithm to Nick Gould return a linear ordering of all the points, which may be Numerical Analysis Group impossible to achieve faultlessly with a preference function Rutherford Appleton Laboratory in general non-transitive. [email protected] Mehryar Mohri Courant Institute of Mathematical Sciences & Google Dominique Orban Research Ecole Polytechnique de Montreal [email protected] [email protected]

Daniel Robinson MS52 Oxford University Label Ranking through Soft Projections onto Poly- [email protected] hedra In the talk we focus on the problem of learning to rank MS50 labels from a real valued feedback associated with each la- A Regularized Primal-Dual SQP Method bel. We cast the feedback as a preferences graph where the nodes of the graph are the labels and edges express We present a regularized SQP method based on a primal- preferences over labels. We tackle the learning problem by dual augmented Lagrangian function. Trial steps are com- defining a loss function for comparing a predicted graph puted from carefully chosen subproblems that utilize re- with a feedback graph. This loss is materialized by decom- lationships between traditional SQP, stabilized SQP, and posing the feedback graph into bipartite sub-graphs. We the augmented Lagrangian. Each subproblem is well de- then adopt the maximum-margin framework which leads to fined regardless of the rank of the Jacobian, and (to some a quadratic optimization problem with linear constraints. extent) we challenge the belief that large penalty parame- While the size of the problem grows quadratically with the ters should be avoided. Numerical results on equality con- number of the nodes in the feedback graph, we derive a strained problems from the CUTEr test set are provided. problem of a significantly smaller size and prove that it at- 136 OP11 Abstracts

tains the same minimum. We then describe an efficient al- pal Component Analysis gorithm, called SOPOPO, for solving the reduced problem by employing a soft projection onto the polyhedron defined Many data-related applications utilize principal component by a reduced set of constraints. We also describe and ana- analysis and/or data dimension reduction techniques that lyze a wrapper procedure for batch learning when multiple require efficiently computing leading parts of singular value graphs are provided for training. We conclude with the decompositions (SVD) of very large matrices. In this talk, description of experiments and applications that demon- we introduce a subspace iteration scheme that uses limited strate the merits of SOPOPO. Based on joint work with memory Krylov subspace optimization to do acceleration. Shai Shalev-Shwartz and Samy Bengio. For more details We present extensive numerical results comparing a Matlab and code see http://www.magicbroom.info/Research.html implementation of the algorithm with state-of-the-art SVD solvers. Our tests indicate that the proposed method can Yoram Singer provide better performance under the Matlab environment Google Research over a wide range of problems. [email protected] Xin Liu CAAM MS52 RICE UNIVERSITY Ranking by Pairwise Comparison: Choice of [email protected] Method can Produce Arbitrarily Different Rank Order MS53 For the three methods Principal Eigenvector, HodgeRank Feasible Methods for Optimization with Orthogo- and Tropical Eigenvector for obtaining cardinal ranking nality Constraints: Part II from a paired comparison matrix, we proved the following: for all n>3, for any rank order pair (σ1,σ2), there ex- We extended the gradient approaches for minimization ists a comparison matrix in which one method gives the with orthogonality constraints from two perspectives. ranking σ1, and another method gives the ranking σ2.We First, a limited-memory BFGS method is proposed without discuss the implications of this result in practice, study the using the expensive parallel translation or vector transport. geometry of the methods, and state some open problems. Second, in order to handle general constraints, we embed the orthogonality constraint preserving approaches in the Ngoc Mai Tran augmented Lagrangian framework. Numerical experiments University of California, Berkeley on a variety of problems are presented. [email protected] Zaiwen Wen Shanghai Jiao Tong University MS53 Department of Mathematics Hyperspectral Data Unmixing using Compressive [email protected] Sensing—Method and Real-Data Simulations

Hyperspectral data unmixing typically demands enormous MS53 computational resources in terms of storage, computation Feasible Methods For Optimization with Orthogo- and I/O throughputs, especially for real-time processing. nality Constraints: Part I

In light of the emerging field compressive sensing, we investigate a low complexity scheme for hyperspectral data Minimization with orthogonality constraints (e.g., X X = acquisition and reconstruction. Specifically, compressed I) and/or spherical constraints (e.g., x2 =1)haswide hyperspectral data are acquired directly by a device sim- applications in polynomial optimization, combinatorial op- ilar to the single-pixel camera. Instead of firstly collect- timization, eigenvalue problems, matrix rank minimiza- ing the pixels/voxels, it acquires the random projections tion, etc. To deal with these difficulties, we propose to of a scene based on the principle of compressive sensing. useaCrank-Nicolson-likeupdateschemetopreservethe To decode the compressed data, we propose a numerical constraints and, based on it, develop a curvilinear search procedure to straightly compute the unmixed abundance algorithm. Preliminary numerical experiments on a wide fractions of given endmembers, completely bypassing high- collection of problems show that the proposed algorithm is complexity tasks involving the hyperspectral data cube it- very promising. self. Grounded on the former work of splitting idea and TVAL3 algorithm, an augmented Lagrangian type algo- Wotao Yin rithm is developed to solve the unmixing model. In prac- Rice University tice, either the observed data or the priori info may contain [email protected] disturbance or noise, which causes the trouble of unmixing. Experimental and computational results show that MS54 the proposed scheme has a high potential in real-world applications, even if the noise exists. Implementation of a Predictive Controller on an FPGA Chengbo C. Li Rice University Predictive control is an advanced control technique that Dept of Comp and Applied Math relies on the solution of a convex QP at every sample in- [email protected] stant. In order to apply predictive control at faster sampling rates, there is a need for faster methods for solving the optimization problems. We present an FPGA implementa- MS53 tion of an interior-point solver, which provides substantial A Simple and Efficient SVD Algorithm for Princi- acceleration over a sequential CPU implementation. In addition, the proposed architecture possesses special features that increase the potential performance benefit by an extra OP11 Abstracts 137

order of magnitude. distributed computation architecture.

Juan L. Jerez, George Constantinides, Eric C. Kerrigan Ion Necoara, Ioan Dumitrache, Valentin Nedelcu Imperial College London University Politehnica Bucharest [email protected], [email protected], [email protected], [email protected], [email protected] [email protected] MS55 MS54 Warmstarting Interior-Point Methods for SDP in A Well-conditioned Interior Point Method with an the Cutting-Plane Method Application to Optimal Control We present our recent progress with warmstarting succes- We propose an approximate method for computing the sive SDP relaxations in cutting-plane schemes for combina- search direction at each iteration of an interior point torial optimization problems. Following previous advances method. If the ratio of the slack variable and dual variable of interior-point warmstarts for LP, we show how to gen- associated with a constraint is above a given threshold, eralize such strategies for SDP and explore their computa- the KKT system is modified in an appropriately-defined tional promise and effectiveness. We also plan to address way. We show that the condition number of the KKT ma- the problem of warmstarting SDP after data perturbations trix is improved and that the method performs favorably, and propose a set of test problems to be used as warmstart- compared to existing methods, when solving constrained ing benchmarks. optimal control problems. Alexander Engau Amir Shahzad, Eric C. Kerrigan, George Constantinides University of Colorado, Denver, USA. Imperial College London [email protected] [email protected], [email protected], [email protected] MS55 Warmstaring Interior Point Strategies for Combi- MS54 natorial Optimization Applications Multiple Shooting for Large-Scale Systems When solving a sequence of closely-related problems, We propose a variant of the standard multiple shooting warmstaring strategies are essential. In recent years sev- method which takes into account the structure of certain eral of these techniques have been proposed for interior large-scale systems in order to obtain a better controller point methods. In this talk, we present some of these tech- design flexibility and high parallelizability. We solve large- niques and propose new warmstarting strategies applicable scale optimal control problems by making use of adjoint- in a column generation framework. We compare them with based sequential quadratic programming. A numerical ex- other strategies in the literature when solving combinato- periment shows that this can lead to considerable savings rial optimization problems. Our preliminary results sug- in computational time for the sensitivity generation. gest that an efficient warmstarting strategy offers savings in both, time and iterations. Carlo Savorgnan, Attila Kozma Department of Electrical Engineering Pablo Gonzalez-Brevis KU Leuven, Belgium School of Mathematics [email protected], [email protected] [email protected] Jacek Gondzio Joel Andersson The University of Edinburgh, United Kingdom Electrical Engineering Department [email protected] K.U.Leuven [email protected] MS55 Moritz Diehl Approximate Solutions of SDP Relaxations K.U.Leuven [email protected] Interior point methods for semidefinite programs are limited in the size of instances they can solve, so many alternative approaches have been developed. These may lead MS54 to solutions that satisfy the positive semidefiniteness re- Distributed Optimization Methods for Large - quirement only in the limit. Randomization techniques are Scale Control Problems often applied to the SDP solution to provide a solution to an underlying problem. We quantify the effect of solving In this paper we analyze the optimization-theoretic con- the SDP approximately on the quality of the randomized cepts of parallel and distributed methods for solving large- solution for some problem classes. scale coupled optimization problems and demonstrate how several estimation and control problems related to complex Tim Lee network systems can be formulated in these settings. The Dept of Mathematical Sciences paper presents a systematic framework to exploit the po- Rensselaer Polytechnic Institute tential of the decomposition structures as a way to obtain [email protected] different parallel algorithms, each with a different tradeoff among convergence speed, message passing amount, and John E. Mitchell Rensselaer Polytechnic Institute 138 OP11 Abstracts

110, 8th Street, Troy, NY, 12180 MS56 [email protected] Optimal Design of System Architectures Design of large complex systems (e.g. buildings, dis- MS55 tributed power systems, transportation networks, etc.) has Solving Combinatorial Optimization Problems been challenging due to the huge design space, non-linear with Interior Point Methods discontinuous dynamic behavior, and uncertainties operational scenarios unknown during the design phase. These A wealth of solution methods is available for solving com- problems fall in the class of non-convex mixed integer non- binatorial optimization problems. Focusing on general- linear programs which is an active area of research. In this purpose exact methods based on integer programming talk, we will present a two phase optimization approach - models, the standard approaches rely on solving a sequence Comprehensive Screening (CS) and High Fidelity Evalua- of closely related linear programming problems. In this tion (HFE) for the optimal design of large systems with talk, we address the challenging issues of using a primal- speciﬁc application to microgrid architectures. In the CS dual interior point method within a branch-and-price-and- phase, a mixed integer linear program (MILP) representa- cut strategy, and present preliminary computational results tion is used to mathematically capture the space of design for classical combinatorial optimization problems from the alternatives. Key to this is the assumption of linear mod- literature. els for the components in the system. The HF phase uses the optimal architecture and nonlinear model for the com- Pedro Munari ponents to determine the optimal sizing and dispatching University of Sao Paulo, Brazil decisions. In this talk, we will overview the methodology [email protected] when applied to the design of energy supply systems that would minimize lifecycle costs while meeting a given electri- Jacek Gondzio cal and thermal demand pattern. We will also investigate The University of Edinburgh, United Kingdom approaches for including uncertainty in input variables. [email protected] Arvind Raghunathan, Niranjan Desai, Ritesh Khire, Stella Oggianu, Xin Wu, Shui Yuan, Larry Zeidner MS56 United Technologies Research Center A Parallel Framework for Identifying Vulnerabili- [email protected], [email protected], ties in the Electric Power Grid [email protected], [email protected], [email protected], [email protected], Identifying multiple contingencies of an electric power grid [email protected] requires the solution of a large bilevel optimization problem, which is computationally expensive. We explore a parallel branch-and-bound framework that exploits the dis- MS56 creteness of the outer-level variables instead of relaxing Title: Multi-stage Stochastic Decomposition with them to continuous ones. The framework is nicely decou- Applications in Energy Systems Planning pled in the sense that it allows various optimal power ﬂow (OPF) algorithms to be used for the inner-level load shed- Many energy systems planning require that they be inte- ding problem. We evaluate our framework on a real-sized grated with simulators that are capable of providing sam- problem. ple paths over hours, and sometimes days. However, most stochastic programming algorithms are designed to use a Juan C. Meza collection of scenarios rather than working with sample Lawrence Berkeley National Laboratory paths, one at a time. We will discuss a multi-stage version [email protected] of Stochastic Decomposition which allows us to integrate outputs from a simulator directly into the planning model. Aydin Buluc Applications in power system planning and operations will Lawrence Berkeley Lab be discussed. [email protected] Suvrajeet Sen Integrated Systems Eng MS56 Ohio State Univ MOPEC Models for Energy Problems [email protected]

We consider MOPEC models: collections of optimization problems linked by equilibrium (or complementarity) con- MS57 straints. We show the relevance of this modeling framework Identification of an Unknown Parameter in the to a number of different problems associated with energy Main Part of an Elliptic PDE planning, and detail several algorithms for their solution. The model will incorporate stochastic effects, contracts, Identification of an Unknown Parameter in the Main Part and the possibility of retention of goods. of an Elliptic PDE We are interested in identifying an unknown material parameter a(x) in the main part of an el- Michael C. Ferris liptic partial differential equation University of Wisconsin Department of Computer Science −div (a(x)grady(x)) = g(x)inΩ [email protected] with corresponding boundary conditions. We discuss a Ti- Roger Wets chonov regularization University of California, Davis 2 2 [email protected] min J(y,a)=y − ydL2(Ω) + αaHs(Ω) a OP11 Abstracts 139

with s>0. Moreover, we require the following constraints ciency oft he proposed methods. for the unknown parameter Barbara kaltenbacher University of Graz 0

Bissan Ghaddar complexity requires new approaches to quantifying and University of Waterloo controlling complexity. We investigate techniques aimed [email protected] at modeling complexity computationally based on nonlinear programming formulations, as well as algorithms for Miguel F. Anjos handling complexity from a variety of spatial and tempo- Mathematics and Industrial Engineering & GERAD ral perspectives. Ecole´ Polytechnique de Montréal Natalia Alexandrov [email protected] NASA Langley Research Center [email protected] MS58 Computing General Static-arbitrage Bounds for MS59 European Basket Options via Dantzig-Wolfe De- Excursions into Multi-disciplinary Design under composition Uncertainty in Aerospace Engineering We study the problem of computing general static- This presentation will discuss the application of design un- arbitrage bounds for European basket options; that is, der uncertainty techniques within the context of multi- computing bounds on the price of a basket option, given disciplinary aerospace systems. We pay particular atten- the only assumption of absence of arbitrage, and information to both the design of supersonic low-boom aircraft and tion about prices of other European basket options on the of hypersonic propulsion systems where multiple disciplines same underlying assets and with the same maturity. In (aerodynamics, acoustics, turbulence, combustion) need to particular, we provide a simple efficient way to compute be considered and where both aleatory and epistemic un- this type of bounds by solving a large finite non-linear pro- certainties are present. The results of our designs focus on gramming formulation of the problem. This is done via both robust and reliable outcomes. a suitable Dantzig-Wolfe decomposition that takes advantage of an integer programming formulation of the corre- Juan J. Alonso sponding subproblems. Department of Aeronautics and Astronautics Our computation method equally applies to both up- Stanford University per and lower arbitrage bounds, and provides a solution [email protected] method for general instances of the problem. This constitutes a substantial contribution to the related literature, in which upper and lower bound problems need to MS59 be treated differently, and which provides efficient ways to Evaluation of Mixed Continuous-discrete Surrogate solve particular static-arbitrage bounds for European bas- Approaches ket options; namely, when the option prices information used to compute the bounds is limited to vanilla and/or Evaluating the performance of surrogate modeling ap- forward options, or when the number of underlying assets proaches is essential for determining their viability in opti- is limited to two assets. mization or uncertainty analysis. To this end, we evaluated Also, our computation method allows the inclusion of real- categorical regression, ACOSSO splines, and treed GPs on world characteristics of option prices into the arbitrage a set of test functions. We describe the principles and bounds problem, such as the presence of bid-ask spreads. metrics we used for this evaluation, the characteristics of We illustrate our results by computing upper and lower the test functions we considered, and our software testbed. arbitrage bounds on gasoline/heating oil crack spread op- Additionally, we present our numerical results and discuss tions. our observations regarding the merits of each approach. Luis F. Zuluaga Patricia D. Hough University of New Brunswick Sandia National Laboratories [email protected] [email protected]

Javier Pena Laura Swiler Carnegie Mellon University Sandia National Laboratories [email protected] Albuquerque, New Mexico 87185 [email protected] Xavier Saynac Faculty of Business Administration Herbie Lee University of New Brunswick University of California, Santa Cruz [email protected] Dept. of Applied Math and Statistics [email protected] Juan C. Vera Tilburg University Department of Econometrics and Operations Research MS59 [email protected] Direct Search Methods for Engineering Optimiza- tion Problems with General Constraints

MS59 We investigate the behavior of derivative-free direct search Quantifying and Managing Complexity in Trans- methods for nonlinear optimization problems with general port Systems constraints where either the objective or (some of) the constraints are deﬁned by complex simulations. Of particular Growing autonomy and distribution will characterize fu- interest is why derivative-free methods that rely on build- ture air transportation systems. Managing the ensuing ing direct models of the objective encounter diﬃculties – OP11 Abstracts 141

particularly as the number of variables grows – when the distributed gradient methods. constraints are more than just simple bounds on the variables. Jorge Nocedal Department of Electrical and Computer Engineering Robert Michael Lewis Northwestern University College of William & Mary [email protected] Dept. of Mathematics [email protected] Yuchen Wu Google Virginia J. Torczon [email protected] College of William & Mary Department of Computer Science [email protected] MS60 Semismooth Newton Methods with Multi-dimensional Filter Globalization for l1 MS60 Optimization Dynamic Sample Size Selection in Algorithms for Machine Learning The sparsity-promoting properties of l1-regularizations have many important applications. We present a class When solving large-scale machine learning and stochastic of methods for l1-regularized optimization problems that optimization problems, sample size selection is an impor- combine semismooth Newton algorithms with globally con- tant component to consider, given its influence over both vergent descent methods in a flexible way. The accep- efficiency and accuracy. Incorporating dynamic sample tance of semismooth Newton steps is controlled by a multi- sizes may also allow an algorithm’s performance to behave dimensional filter, which efficiently relaxes sufficient de- more capably in implementation, in comparison to a static crease requirements for these steps. Global convergence as sample size. The work that will be presented will suggest well as transition to fast local convergence are investigated. appropriate methods for dynamically improving the sample We conclude with numerical illustrations. size selection. Both numerical and theoretical complexity results shall be presented. Michael Ulbrich Technical University of Munich Gillian Chin Chair of Mathematical Optimization Northwestern University [email protected] [email protected] Andre Milzarek Technische Universitaet Muenchen MS60 Department of Mathematics, TopMath Spectral Gradient Methods for Nonlinear Pro- [email protected] gramming

The development of new software for NLP is described. MS62 There are two main design aims (i) to avoid the use of sec- CasADi - A Tool for Dynamic Optimization ond derivatives, and (ii) to avoid storing an approximate and Automatic Differentiation for Object-oriented reduced Hessian matrix by using a new limited memory Modelling Languages spectral gradient approach based on Ritz values. The basic approach to NLP is that of Robinson’s method, globalised We introduce CasADi, an implementation of automatic by using a filter and trust region, rather than a square differentiation in forward and adjoint mode using a hy- penalty term such as in MINOS. A new code for the lin- brid operator-overloading, source-code-transformation ap- ear constraint subproblem (LCP) has been developed using proach. For maximum efficiency, CasADi works with a the Ritz values approach. Numerical experience will be de- combination of two different graph representations : One scribed. supporting only scalar-valued, built-in unary and binary operations without branching and secondly, a representa- Roger Fletcher tion supporting matrix-valued operations, branchings such University of Dundee as if-statements as well as function calls to arbitrary func- Department of Mathematics & tions (e.g. ODE/DAE integrators). fl[email protected] Joel Andersson Electrical Engineering Department MS60 K.U.Leuven New Methods for Regularized Machine Learning [email protected] and Stochastic Programming

We consider machine learning problems, such as those aris- Moritz Diehl ing in speech recognition, where the number of training K.U.Leuven points can reach into the billions. We describe new on- [email protected] line and distributed gradient methods capable of solving problems of this type. Our methods use regularized logis- MS62 tic models that promote sparse parameters. We demonstrate the efficiency of the proposed methods using a pro- On an Iterative Range Space Method duction system at Google. We also present complexity re- We present several modifications for the total quasi- sults comparing sequential online methods and mini-batch Newton method to solve general nonlinear problems. By the use of low-rank approximation and automatic differ- 142 OP11 Abstracts

entiation, no exact evaluation of the constraint Jacobian for some test problems are shown and the Hessian of the Lagrangian is required in this approach. To make the method more suitable for large scale Andrea Walther optimization we employ a range space factorization using Universität Paderborn well-known limited memory techniques with compact stor- [email protected] age such as L-BFGS and L-SR1. Lorenz T. Biegler Torsten F. Bosse Carnegie Mellon University Humboldt-Universität zu Berlin, USA Institut für Mathematik [email protected] [email protected]

Andreas Griewank MS63 HU Berlin, MATHEON Research Center, Germany Small Chvatal Rank [email protected] We propose a variant of the Chvatal-Gomory procedure that will produce a suﬃcient set of facet normals for the MS62 integer hulls of all polyhedra {x : Ax ≤ b} as b varies. Solving Time-Harmonic Inverse Medium Opti- The number of steps needed is called the small Chvatal mization Problems with Inexact Interior-Point rank (SCR) of A. We characterize matrices for which SCR Step Computation is zero via the notion of supernormality which generalizes unimodularity. SCR is studied in the context of the stable We formulate an inverse medium problem as a PDE- set problem in a graph, and we show that many of the well- constrained optimization problem, where the underlying known facet normals of the stable set polytope appear in wave ﬁeld solves the time-harmonic Helmholtz equation. at most two rounds of our procedure. Our results reveal a Ill-posedness is tackled through regularization while the uniform hypercyclic structure behind the normals of many inclusion of inequality constraints is used to encode prior complicated facet inequalities in the literature for the sta- knowledge. The resulting nonconvex optimization problem ble set polytope. Lower bounds for SCR are derived both is solved by a primal-dual interior-point algorithm with in- in general and for polytopes in the unit cube. exact step computation. Numerical results both in two and three space dimensions illustrate the usefulness of the Tristram Bogart approach. San Francisco State University [email protected] Olaf Schenk Department of Mathematics and Computer Science Annie Raymond University of Basel, Switzerland Berlin Mathematical School [email protected] [email protected]

Marcus Grote Rekha Thomas Universit¨at Basel University of Washington [email protected] [email protected]

Johannes Huber University of Basel MS63 [email protected] Gröbner Bases and Hilbert’s Nullstellensatz: Com- binatorial Interpretations and Algorithmic Tech- Andreas Wächter niques IBM T. J. Watson Research Center [email protected] Systems of polynomial equations with coefficients over an algebraically closed field K can be used to concisely model combinatorial problems. In this way, a combinatorial prob- Frank E. Curtis lem is feasible (e.g., a graph is 3-colorable, hamiltonian, Industrial and Systems Engineering etc.) if and only if a related system of polynomial equations Lehigh University has a solution. We present a collection of results based on [email protected] these non-linear models. In the case of the independent set problem, we present a combinatorial interpretation of the MS62 Hilbert’s Nullstellensatz certificate of infeasibility. In the case of the dominating set problem, we present a combi- On an Inexact Trust-region Approach for Inequal- natorial interpretation of the universal Gröbner basis. In ity Constrained Optimization the case of graph 3-coloring, we demonstrate an algorithm This talk presents a trust-region SQP algorithm for the so- that is surprisingly practical in practice. lution of minimization problems with nonlinear inequality Susan Margulies constraints. The approach works only with an approxima- Computational and Applied Mathematics tion of the constraint Jacobian. Hence, it is well suited for Rice University optimization problems of moderate size but with dense con- [email protected] straint Jacobian. The accuracy requirements for the presented first-order global convergence result can be verified easily during the optimization process. Numerical results OP11 Abstracts 143

MS63 [email protected] The Border Basis Closure The Sherali-Adams lift-and-project hierarchy is a funda- MS64 mental construct in integer programming, which provides A Verification Based Method to Generate Strong successively tighter linear programming relaxations of the Cutting Planes for IPs integer hull of a polytope. We initiate a new approach to understanding the Sherali-Adams procedure by relating it A cutting-plane procedure for integer programming (IP) to methods from computational algebraic geometry. We problems usually involves invoking a black-box procedure present a modified version of the border basis algorithm to compute a cutting plane. In this paper, we describe to generate a hierarchy of linear programming relaxations an alternative paradigm of using the same cutting-plane that are stronger than those of Sherali and Adams, and black-box. This involves two steps. In the first step, we over which one can still optimize in polynomial time (for design an inequality cx ≤ d, independent of the cutting a fixed number of rounds in the hierarchy). In contrast to plane black-box. In the second step, we verify that the designed inequality is a valid inequality by verifying that the the well-known Grbner bases approach to integer program- n n ming, our procedure does not create primal solutions, but set P ∩{x ∈ R : cx ≥ d +1}∩Z is empty using cutting constitutes a novel approach of using computer-algebraic planes from the black-box. (Here P is the feasible region methods to produce dual bounds. of the linear-programming relaxation of the IP.) We refer to the closure of all cutting planes that can be verified to Sebastian Pokutta, Andreas S. Schulz be valid using a specific cutting plane black-box as the ver- Massachusetts Institute of Technology ification closure of the considered black box. This verifica- [email protected], [email protected] tion paradigm naturally leads to the question of how much extra strength one might hope to gain by having an oracle in place that provides us with potential cutting-planes MS63 and we are left with the task of verifying that its output Graver Bases Methods in Integer Programming is valid. We show that cutting-plane obtained via the verification scheme can be very strong, significantly exceed- N-fold integer programming is a fundamental problem with ing the capabilities of the regular cutting-plane procedure. a variety of natural applications in operations research and On the other hand, we present lower bounds on the rank statistics. Moreover, it is universal and provides a new, of verification cutting planes for known difficult infeasible variable-dimension, parametrization of all of integer pro- 0/1 instances, showing that while verification procedure is gramming.We use Graver bases methods to establish an strong, it is not unrealistically so. iterative algorithm that solves this problem in polynomial time. Using it, we also propose a simple Graver approx- Santanu S. Dey imation hierarchy, parameterized by degree, for nonlinear Georgia Institute of Technology integer programming in general and optimization over mul- School of Industrial and System Engineering tiway tables in particular, which makes use of quickly con- [email protected] structible approximations of the true Graver basis. We demonstrate this scheme for approximating the (universal) Sebastian Pukutta integer three-way table feasibility problem. The talk is Sloan School of Management, MIT based on joint work with S. Onn, R. Hemmecke and on my [email protected] thesis in preparation (under the supervision of S. Onn).

Lyubov Romanchuk MS64 Technion - Israel Institute of Technology, Haifa Generating Two-Row Cuts from Lattice-Free Bod- [email protected] ies Andersen et al (2007) and Cornuejols and Margot (2009) MS64 show that facet-defining inequalities of a system with two On Maximally Violated Cuts Obtained from a Ba- constraints and two integer variables are related to maxi- sis mal lattice-free convex sets. We give an algorithm to construct those sets, thereby enumerating all facet-defining Most cuts used in practice can be derived from a basis and T ≥ inequalities for such systems. Computational results are are of the form α x 1, where x is a vector of non-basic presented. variables and α ≥ 0. Such cuts are called maximally vio- T lated wrt a pointx ¯ ≥ 0ifα x¯ = 0. In an earlier paper Kenneth Chen we presented computational results for maximally violated GeorgiaTech cuts derived from an optimal basis of the linear relaxation. [email protected] In this talk we also consider pivoting and deriving maximally violated cuts from alternative non-optimal bases. William Cook Kent Andersen Georgia Institute of Technology University of Aarhus [email protected] [email protected] Ricardo Fukasawa Adam N. Letchford University of Waterloo Lancaster University Management School [email protected] [email protected] Daniel Steffy Robert Weismantel GeorgiaTech ETH Zuerich desteff[email protected] 144 OP11 Abstracts

MS64 Regularized Matrix Least Squares Problems Approximating the Split Closure We introduce a proximal point algorithm for solving nu- The first split closure has been proven in practice to be a clear norm regularized matrix least squares problems with very tight approximation of the ideal convex hull formula- equality and inequality constraints. The inner subprob- tion of a generic Mixed Integer Program (MIP). However, lemsaresolvedbyaninexactsmoothingNewtonmethod, exact separation procedures for optimizing over it have un- which is proved to be quadratically convergent under a con- acceptable computing times. We present heuristic proce- straint non-degenerate condition, together with the strong dures for approximating the split closure of a MIP, as well semi-smoothness property of the singular value threshold- as algorithmic techniques for speeding up such separation. ing operator. Numerical experiments on problems arising Preliminary computational results show the effectiveness from low-rank approximations of transition matrices show of the proposed procedures compared to the state of the that our algorithm is efficient and robust. art. Kaifeng Jiang Matteo Fischetti, Domenico Salvagnin Department of Mathematics University of Padova National University of Singapore, Singapore fi[email protected], [email protected] [email protected]

Defeng Sun MS65 Dept of Mathematics Flexible First-order Methods for Rank Minimiza- National University of Singapore tion [email protected]

We describe a flexible framework for solving constrained Kim-Chuan Toh non-smooth convex programs, such as nuclear norm mini- National University of Singapore mization and LASSO. The technique is based on smooth- Department of Mathematics and Singapore-MIT Alliance ing and solving the dual formulation. An advantage of the [email protected] technique is that it allows for many variations, such as a robust-PCA formulation. We also discuss the special case where the solution is known to be PSD, which occurs in MS66 covariance estimation and quantum tomography. A Bilevel Optimization Approach to Obtaining Op- Stephen Becker timal Cost Functions for Human Arm Movements California Institute of Technology It is known that human motions are (approximately) op- [email protected] timal for suitable, unknown cost functions subject to the dynamics. We use bilevel optimization to investigate the Ewout van den Berg following inverse problem: Which cost function out of a Stanford University parameterized family composed from functions suggested [email protected] in the literature reproduces recorded human arm movements best? The lower level problem is an optimal control problem governed by a nonlinear model of the human arm MS65 dynamics. Promising applications are also discussed. Fast First-Order and Alternating Direction Meth- ods for Stable Princial Component Pursuit Sebastian Albrecht, Marion Leibold Technische Universitaet Muenchen Given a matrix M that is the sum of a low rank matrix [email protected], [email protected] X and a sparse matrix Y, it is known that under certain conditions, X and Y can be recovered with very high prob- Michael Ulbrich ability by solving a so-called robust principal component Technical University of Munich pursuit problem. When M has noise added to it, the recov- Chair of Mathematical Optimization ery problem is called stable principal component pursuit. [email protected] In this problem one minimizes the sum of the nuclear norm of X plus a scalar times the sum of the absolute values of the elements of Y, subject to the Frobenius norm of X+Y- MS66 M being less than some known noise level. We show how Optimality Conditions for Bilevel Programming to apply Nesterov’s optimal gradient and composite methods and a fast alternating linearization method to obtain Bilevel programming problems are hierarchical optimiza- epsilon-optimal solutions in O(1/epsilon) iterations, while tion problems where the feasible region is (in part) re- keeping the cost of each iteration low. We also propose an stricted to the graph of the solution set mapping of a second alternating direction augmented Lagrangian method that parametric optimization problem. To solve them and to deis extremely efficient, for which we prove convergence. rive optimality conditions for these problems this parametric optimization problem needs to be replaced with its (nec- Don Goldfarb,NecdetAybat essary) optimality conditions. This results in a (one-level) Columbia University optimization problem. In the talk different approaches to [email protected], [email protected] transform the bilevel programming will be suggested and the relations between the original bilevel problem and the MS65 one replacing it will be investigated. The resulting (necessary) optimality conditions will be formulated. A Proximal Point Algorithm for Nuclear Norm Stephan Dempe Technical University of Freiberg OP11 Abstracts 145

09596 Freiberg, Germany are used to solve this problem. [email protected] Sandrine Charousset Alain B. Zemkoho EDF Research Instiut of Numerical Mathematics and Optimization [email protected] TU Bergakademie Freiberg [email protected] MS67 The Value of Rolling Horizon Policies for Risk- MS66 averse Hydro-thermal Planning Mathematical Programs with Vanishing Con- We consider the optimal management of a hydro-thermal straints power system in the mid-term. This is a large-scale mul- A new class of constrained optimization problems called tistage stochastic linear program, often solved by combin- mathematical programs with vanishing constraints (MPVC) ing sampling with decomposition algorithms, like stochas- is considered. This type of problem is known to act as a tic dual dynamic programming. However, such method- unified framework for several problems from topology opti- ologies may entail prohibitive computational time, espe- mization and is hence very interesting from an engineering cially when applied to a risk-averse formulation of the prob- point of view. Moreover, due nonconvexity and violation of lem. For a model that takes into account losses and un- most of the standard constraint qualifications, an MPVC certainty in both the inflows and the demand, we propose is very challenging from a theoretical and numerical view- a risk-averse rolling horizon approach based on subprob- point. In the face of that, problem-tailored constraint qual- lems having deterministic constraints for the current time ifications and the related stationarity concepts are investi- step and future uncertain constraints dealt with as chance gated. Moreover, a numerical approach for the solution of and CVaR constraints. When uncertainty in the problem an MPVC is surveyed. is represented by a periodic autoregressive stochastic process, each subproblem is a medium-size linear program, Tim Hoheisel easy to solve. Being both nonanticipative and feasible, the University of Würzburg resulting risk-averse policy keeps reservoirs above certain 97074 Würzburg, Germany critical levels almost surely. In order to evaluate the ben- [email protected] efits of the rolling horizon approach, we introduce a non- rolling horizon policy, both robust and feasible, based on solutions obtained at the first time step with the rolling MS66 horizon methodology. When applied to a real-life power On the Concept of T-stationarity in MPCC and system, the superiority of the rolling approach becomes MPVC evident, compared both to the non-rolling horizon policy aforementioned and to a stochastic dual dynamic program- We call a stationarity concept for a given class of opti- ming strategy, frequently employed for this type of prob- mization problems topologically relevant, if it allows to es- lems. tablish a Morse theory. Recent results about mathematical programs with vanishing constraints (MPVCs) illus- Vincent Guigues trated that the topologically relevant stationarity concept PUC-Rio is not necessarily one which is already known, in contrast Brazil to finite smooth constrained optimization and MPCCs, [email protected] where KKT stationarity and C-stationarity are topologically relevant, respectively. This motivated the introduc- Claudia Sagastizábal tion of T-stationarity for MPVCs. We point out con- CEPEL nections to numerical methods for MPCCs and MPVCs, [email protected] where KKT points of smooth approximations tend to T- stationary points of the original problems. MS67 Oliver Stein The N-k Problem using AC Power Flows Karlsruhe Institute of Technology 76131 Karlsruhe, Germany Given a power grid, we search for a set of k or fewer lines [email protected] whose simultaneous outage will impact stability. We study this problem under AC power flows; our concepts of ”stability” primarily focus on voltage stability. In our approach MS67 we bypass combinatorial complexity by positing an intel- Optimization Applied to Electricity Generation ligent adversary who can increase the resistance or reac- Management at EdF tance of power lines, within budgets, so as to maximize the resulting instability. This problem is continuous (though We consider the one-day-ahead scheduling of a power mix nonconcave) and thus, amenable to continuous optimiza- with about 150 thermal plants and 50 hydro-valleys, as to tion techniques. We report on experiments using large, ensure offer and demand equilibrium at minimal cost, while real-world grids. satisfying the technical constraints of all plants. From the optimization point-of-view, the problem is quite difficult Sean Harnett because it must be solved in less than 15 minutes; but Columbia University it is large-scale, with 106 mixed-integer variables and 106 [email protected] nonconvex and discontinous constraints. We focus on the latest developments about the optimisation methods that Daniel Bienstock Columbia University IEOR and APAM Departments IEOR Department 146 OP11 Abstracts

[email protected] tical reconstruction schemes.

Bastian Harrach MS67 Department of Mathematics - M1 Security Constrained Optimization for Electric Technische Universit¨at M¨unchen Power Systems [email protected]

The need for improving security standards for electric power systems is well recognized. Such efforts however, MS68 are hindered by lack of decision support tools that can in- Nonsmooth Regularization and Sparsity Optimiza- corporate security into the decision making process. The tion current practice is to protect the system against known or anticipated failures either by using a post-processing The sparsity optimization for the linear least square prob- phase or by explicit enumeration of the know cases. These lem is considered. The problem is formulated as non- approaches not only lack scalability to larger systems or smooth regularization problem. The necessary optimality higher security standards, but also are limited to predicted condition is derived and a numerical algorithm to deter- failures, which is a significant shortcoming with the uncer- mine a solution is developed and analyzed. The property tainty of the renewable generation. In our earlier work, we of solutions and the optimal value function as a function have developed efficient techniques for vulnerability analy- of the regularization parameter is analyzed. Various se- sis of electric power systems. We are now in the process of lection principle and algorithms for determining the reg- adding our vulnerability analysis techniques into the deci- ularization parameter are developed and analyzed for the sion making process. Specifically, we are investigating an sparisity regularization based on the analysis of the optimal alternative formulation of security-constrained unit com- value function. mitment problem. The key to our approach is our ability to compactly represent security constraints. In this talk, Kazufumi Ito we will present our security formulations, and our results North Carolina State University for solving the security-constrained unit-commitment prob- Department of Mathematics lem. [email protected]

Ali Pinar Sandia National Labs MS68 [email protected] Error Estimates for joint Tikhonov and Lavrentiev Regularization of Parameter Identification Pro- Jean-Paul Watson belms Sandia National Laboratories Problems of optimal control often involve constraints both Discrete Math and Complex Systems on the control and on the state of the system, but the so- [email protected] lution may not be stable to calculate. Hence, one often employs Tikhonov regularization. Then the resulting opti- MS68 mization problem may still be difficult to solve due to low regularity of Lagrange multipliers. This difficulty can be L1 Fitting for Nonlinear Parameter Identification overcome by Lavrentiev-type regularization. In this talk. Problems for PDEs error estimates for this kind of doubly regularized problems For parameter identification problems where the measured are derived. data is corrupted by impulsive noise, L1-data fitting is 2 Dirk Lorenz more robust than conventional L -fitting. However, this Technical University of Braunschweig leads to a non-smooth optimization problem. In this talk, [email protected] an approach for the numerical solution of parameter identification for PDEs with L1-data fitting is presented and analyzed. This approach is based on a semi-smooth Newton Arnd Rösch method and shows locally superlinear convergence. The University of Duisburg-Essen effectiveness is illustrated through numerical examples. [email protected]

Christian Clason University of Graz MS69 Institute for Mathematics and Scientific Computing On Some Strategies for Jacobian-free Precondition- [email protected] ing of Sequences of Nonsymmetric Linear Systems An appealing property of Newton-Krylov methods for MS68 the solution of nonlinear algebraic systems is that they Simultaneous Identification of Multiple Coeffi- lend themselves well for matrix-free implementations where cients in an Elliptic PDE multiplication with the Jacobian is replaced by a difference approximation. However, this makes the computation of We consider the inverse problem of determining multi- robust LU-type preconditioners for the Jacobians signifi- ple, piecewise analytic coefficients in an elliptic PDE from cantly more challenging. In this talk we address various boundary measurements. Based on the theory of localized matrix-free preconditioning techniques for the special case potentials, we are able to give an exact theoretical char- where we wish to update preconditioners from previous lin- acterization of the reconstructible information. We also ear systems. discuss the consequences of this injectivity result to prac- Jurjen Duintjer Tebbens Institute of Computer Sciences Academy of Sciences of the Czech Republic, Prague OP11 Abstracts 147

[email protected] PDE-Constrained Optimization

Miroslav Tuma We investigate the application of parallel multilevel Academy of Sciences of the Czech Republic domain-decomposition preconditioners to linear systems Institute of Computer Science arising from the discretization of optimality systems for [email protected] elliptic optimal control problems. We focus on algebraic multilevel Schwarz preconditioners with smoothed aggregation coarsening, that are modified to take into account MS69 the block structure that results from a suitable ordering of Limited-memory Preconditioners for Large Sparse the unknowns. We report results of numerical experiments Least-squares Problems performed on linux clusters with the MLD2P4 package, extended to include the above modifications. We present a technique for constructing incomplete LDLT preconditioners for the normal equation matrix of large Alfio Borzi’ and sparse linear least-squares problems. The precondi- University of Sannio tioners obtained can be interpreted as approximate sparse Department of Engineering inverse preconditioners. The construction of the precondi- alfi[email protected] tioners is breakdown-free and does not need to form the normal matrix. Only matrix-vector products are required Valentina De Simone, Daniela di Serafino and transpose-free implementations are possible. The den- Second University of Naples sity and sparsity pattern is fixed in advanced and limited Department of Mathematics intermediate storage is needed. Numerical experiments are [email protected], shown. daniela.diserafi[email protected] Benedetta Morini Universita’diFirenze MS70 benedetta.morini@unifi.it Ambiguous Probabilistic Set Covering

Stefania Bellavia We consider probabilistic set covering constraints, where Universita di Firenze the covering coefficients are Bernoulli random variables stefania.bellavia@unifi.it with partial distribution information. Using union bounds, we formulate the corresponding ambiguous probabilistic set covering problem into a deterministic mixed-integer linear Jacek Gondzio program. Some strong valid inequalities for the problem The University of Edinburgh, United Kingdom are also developed. [email protected] Shabbir Ahmed H. Milton Stewart School of Industrial & Systems MS69 Engineering Multipreconditioned GMRES with Applications in Georgia Institute of Technology PDE-constrained Optimization [email protected] The bottleneck in many algorithms for solving large scale optimization problems is the solution of a saddle point sys- Dimitri Papageorgiou tem. A common way to do this is by using a Krylov sub- ISyE space method, which needs to be coupled with a suitable Georgia Tech preconditioner to be effective. For a saddle point problems [email protected] there are a number of possible choices of preconditioner – e.g. constraint or block diagonal preconditioners – and MS70 in certain cases one or another may be a better choice. In this talk we present multipreconditioned GMRES (MPGM- On the Complexity of Non-Overlapping Multivari- RES), which is an algorithm that extends GMRES by auto- ate Marginal Bounds for Probabilistic Combinato- matically combining the properties of more than one pre- rial Optimization Problems conditioner in an optimal way. We will demonstrate the Given a probabilistic combinatorial optimization problem, effectiveness of the algorithm by applying it to systems we evaluate the tightest bound on the expected opti- from problems in PDE-constrained optimization. mal value over joint distributions with given multivariate Tyrone Rees marginals. This bound was first proposed in the PERT Department of Computer Science, context by Meilijson and Nadas (Journal of Applied Prob- University of British Columbia, Canada ability, 1979). New instances of polynomial time com- [email protected] putable bounds are identified. An important feature of the bound we propose is that it is exactly achievable by a joint distribution, unlike many of the existing bounds. Chen Greif Department of Computer Science Karthik Natarajan The University of British Columbia Department of Management Sciences [email protected] City University of Hong Kong [email protected] MS69 Xuan Vinh Doan Parallel Algebraic Multilevel Preconditioners for Department of Combinatorics and Optimization University of Waterloo 148 OP11 Abstracts

[email protected] Nonlinear-Least Squares Problems

We consider the Gauss-Newton algorithm for solving non- MS70 linear least-squares problems, regularized with a quadratic Multiple Objectives Satisficing under Uncertainty term, that occur in data assimilation with application to Meteorology or Oceanography. Each quadratic problem of We propose a class of functions, called multiple objective the method is solved with a dual space conjugate-gradient- satisficing (MOS) criteria, for evaluating the level of com- like method. The use of an effective preconditioning tech- pliance of the objectives in meeting their targets collec- nique is proposed and refined convergence bounds derived, tively under uncertainty. The MOS criteria include the which results in a practical solution method. Finally, stop- joint targets’ achievement probability (success probability ping rules adequate for a trust-region solver are proposed criterion) as a special case and also extend to situations in the dual space. when the probability distribution is not fully characterized or ambiguity. We focus on a class of MOS criteria Serge Gratton that favors diversification, which has the potential to mit- CERFACS igate severe shortfalls in scenarios when an objective fails Toulouse, France to achieve its target. Naturally, this class excludes suc- [email protected] cess probability and we propose the shortfall-aware MOS criterion (S-MOS), which is diversification favoring and is a lower bound to success probability. We show how to MS71 build tractable approximations of S-MOS that preserves Infeasibility Detection in Nonlinear Programming the salient properties of MOS. We report encouraging computational results on a refinery blending problem in meet- We describe an interior point algorithm with infeasibility ing specification targets even in the absence of full distri- detection capabilities. By employing a feasibility restora- butional information. tion phase, the new algorithm can give promote fast convergence to infeasible stationary points, or when the problem Melvyn Sim is feasible, fast convergence to a KKT point. We also de- NUS Business School scribe analysis that shows how two-step active set methods [email protected] that base the step computation on an appropriate model of the penalty function, can give fast infeasibility detection.

MS70 Figen Oztoprak On Safe Tractable Approximations of Chance Con- Sabanci Univeristy strained Linear Matrix Inequalities with Partly De- fi[email protected] pendent Perturbations In this talk, we will demonstrate how tools from probabil- MS71 ity theory can be used to develop safe tractable approx- Updating Rules for the Regularization Parameter imations of chance constrained linear matrix inequalities in the Adaptive Cubic Overestimation Method with partly dependent data perturbations. An advantage of our approach is that the resulting safe tractable approx- The Adaptive Cubic Overestimation method has been re- imations can be formulated as SDPs or even SOCPs, thus cently proposed for solving unconstrained minimization allowing them to be solved easily by off-the-shelf solvers. problems. At each iteration, the objective function is re- We will also discuss some applications of our results. placed by a cubic approximation which comprises an adaptive regularization parameter that estimates the Lipschitz Anthony So constant of the objective. We present new updating strate- The Chinese University of Hong Kong gies for this parameter based on interpolation techniques [email protected] which improve the overall numerical performance of the algorithm. Numerical experiments on large nonlinear least- squares problems are shown. MS71 Derivitive Approximation in Optimization for Sta- Nick Gould tistical Learning Numerical Analysis Group Rutherford Appleton Laboratory Optimization problems that occur in machine learning are [email protected] difficult mainly because of the expense of computing gradient and function values for large data sets. We discuss use Margherita Porcelli of algorithms based on standard concepts such as truncated Department of Mathematics and naXys Newton, that use small-sample approximations to gradi- FUNDP - University of Namur ents and Hessians. We compare them to some of the special [email protected] purpose machine learning algorithms that have been developed. We present computational experiments on some Philippe L. Toint examples and also give some complexity results. The University of Namur Department of Mathematics Richard H. Byrd [email protected] University of Colorado [email protected] MS72 MS71 Semidefinite Relaxations for Non-Convex Preconditioning and Globalizing Conjugate Gra- dients in Dual Space for Quadratically Penalized OP11 Abstracts 149

Quadratic Mixed-Integer Programming Alberto Caprara, Fabio Furini DEIS - University of Bologna We present semidefinite relaxations for unconstrained non- [email protected], [email protected] convex quadratic mixed-integer optimization problems. These relaxations yield tight bounds and are computa- Marco Luebbecke tionally easy to solve for medium-sized instances, even if RWTH, Aachen University some of the variables are integer and unbounded. In this [email protected] case, the problem contains an infinite number of linear constraints; these constraints are separated dynamically. We use this approach as the bounding routine in an SDP-based Enrico Malaguti branch-and-bound framework. In case of a convex objec- DEIS - University of Bologna tive function, the new SDP bound improves the bound [email protected] given by the continuous relaxation of the problem. Numer- ical experiments show that our algorithm performs well on Emiliano Traversi various types of non-convex instances. University of Bologna [email protected] Christoph Buchheim TU Dortmund [email protected] MS72 Computational Evaluation of Verification Cuts

Angelika Wiegele T { An inequality c x ≤ d with integral coefficients for an inte- Alpen-Adria-Universit T ≥ ”a}t Klagenfurt ger program yields a verification cut if c x d+1 contains Institut f. Mathematik no solution to the integer program. Verification cuts can be [email protected] shown to yield strong cuts in many cases. We investigate the computational use of these cuts. Different methods to produce a base inequality cT x ≤ d and different ways to MS72 prove infeasibility of the complementary cut via truncated Safe Coloring of Large Graphs branch-and-cut are considered.

One of the best methods for determining the chromatic Marc E. Pfetsch number of a graph is the linear-programming branch and TU Braunschweig price technique. We present an implementation of the [email protected] method that provides numerically safe results, independent of the floating-point accuracy of the LP solver. We pro- Santanu Dey pose an improved branch-and-bound algorithm for finding Georgia Tech maximum-weight stable sets that enables us closing previ- [email protected] ously open DIMACS benchmarks. Finally, computational results on standard benchmarks as well as an application Sebastian Pokutta from VLSI-design are presented. Massachusetts Institute of Technology [email protected] Stephan Held University of Bonn [email protected] MS73 Regularization and Shifted Barriers for Linear Pro- Edward Sewell gramming Southern Illinois University Edwardsville [email protected] We consider the classical problem of solving a linear program. Our concern is regularization of the problem by William Cook shifted barriers and quadratic penalties. We discuss the Georgia Institute of Technology use of regularizations based on different norms. In addi- [email protected] tion, we discuss how to solve the problem by a primal-dual approach based on simplex-like steps or an interior method.

MS72 Anders Forsgren Dantzig-Wolfe Reformulations of General Mixed Integer Programs Royal Institute of Technology (KTH) Dept. of Mathematics We discuss how Dantzig-Wolfe reformulations can be ap- [email protected] plied to general Mixed Integer Programs (MIP), which do not necessarily have an explicit or implicit block-diagonal MS73 structure, so as to obtain stronger formulations. We show that by looking for almost block-diagonal structures, ap- Incremental Newton-type Methods for Data Fit- plication of Dantzig-Wolfe reformulation leads to improved ting results with respect to the direct application of a general In many structured data-fitting applications, frequent data MIP solver to the original formulation. We briefly discuss access is the main computational cost. Incremental- features which characterize an effective reformulation. gradient algorithms (both deterministic and randomized) Martin Bergner offer inexpensive iterations by sampling only subsets of the RWTH, Aachen University data. These methods can make great progress initially, [email protected] but often stall as they approach a solution. In contrast, 150 OP11 Abstracts

Newton-type methods achieve steady convergence at the formulated in the inﬁnite-dimensional setting or after spa- expense of frequent data access. We explore hybrid meth- tial discretization of the state variables. We will focus on ods that exhibit the beneﬁts of both approaches. Numer- the latter approach, and review methods based on balanced ical experiments illustrate the potential for the approach. truncation as well as Krylov subspace methods for linear and nonlinear problems.

Michael P. Friedlander Peter Benner Dept of Computer Science Max-Planck-Institute for University of British Columbia Dynamics of Complex Technical Systems [email protected] [email protected]

Tobias Breiten MS73 Max-Planck-Institute for Dynamics of Complex Technical A Gauss-Newton-Type Method for Constrained Systems, Magdeburg Optimization Using Differentiable Exact Penalties [email protected] We propose a Gauss-Newton-type method for nonlinear constrained minimization problems, using an extension of MS74 the exact penalty for variational inequalities, introduced Model Reduction Methods in the Calibration of recently by Andre and Silva. The exact penalty is con- Financial Market Models structed based on the incorporation of a multiplier estimate in an augmented Lagrangian. Using a weaker assumption, The calibration of models for derivative pricing is an im- we prove exactness and convergence results. A globaliza- portant application of optimization in finance. The use tion idea is also established, as well as some numerical ex- of reduced order models improves the efficiency of the nu- periments with the CUTE collection. merical scheme substantially. We review various venues for the use of reduced order models and discuss in particular Ellen H. Fukuda proper orthogonal decomposition with a trust region vari- University of So Paulo ant. We illustrate the claims with numerical results for the [email protected] calibration of a PIDE.

PauloJ.S.Silva Ekkehard W. Sachs University of Sao Paulo University of Trier [email protected] Virginia Tech [email protected] Roberto Andreani DMA-IMECC-UNICAMP [email protected] MS74 Applications of DEIM in Nonlinear Model Reduc- tion MS73 Iterative Methods for SQD Linear Systems A dimension reduction method called Discrete Empirical Interpolation (DEIM) is described and shown to dramati- Symmetric quasi-definite (SQD) systems arise naturally cally reduce the computational complexity of the popular in interior-point methods for convex optimization and in Proper Orthogonal Decomposition (POD) method for con- some regularized PDE problems. In this talk we review structing reduced-order models for parametrized nonlinear the connection between SQD linear systems and other re- partial differential equations (PDEs). DEIM is a technique lated problems and investigate their iterative solution. We for reducing the complexity of evaluating the reduced order report on preliminary numerical experience with an imple- nonlinear terms obtained with the standard POD-Galerkin. mentation of a regularization method for convex quadratic POD reduces dimension in the sense that far fewer vari- programming. ables are present, but the complexity of evaluating the nonlinear term remains that of the original problem. DEIM is Dominique Orban a modification of POD that reduces complexity of the non- GERAD and Dept. Mathematics and Industrial linear term of the reduced model to a cost proportional to Engineering the number of reduced variables obtained by POD. The Ecole Polytechnique de Montreal method applies to arbitrary systems of nonlinear ODEs, [email protected] not just those arising from discretization of PDEs. In this talk, the DEIM method will be developed along with a Mario Arioli discussion of its approximation properties. Applications Rutherford Appleton Laboratory in Shape Optimization and PDE constrained optimization Chilton, UK shall be emphasized. Additional applications from Chemi- [email protected] cally Reacting Flow and Neural Modeling will be presented to illustrate the effectiveness and wide applicability of the DEIM approach. MS74 System-theoretic Methods for Model Reduction of Danny C. Sorensen, Saifon Chaturantabut Linear and Nonlinear Parabolic Systems Rice University [email protected], [email protected] We discuss model reduction methods based on ideas from system theory. These methods rely on considering (generalized) transfer functions of the describing state and ob- MS74 servation equations. For parabolic systems, these could be Error Control in POD and RB Discretizations of OP11 Abstracts 151

Nonlinear Optimal Control Problems This extension of the seminal lobbying set-up has important implications: The politician will optimally level the In the talk a-posteriori error estimation is utilized to con- playing field by encouraging weak lobbyists to participate trol Galerkin-based reduced-order models for optimal con- and at least three lobbyists will be active in the leveled trol problems governed by nonlinear partial differential lobbying process. Results are established using the implicit equations. More precisely, the nonlinear problems are programming approach for bilevel problems. treated by an inexact second-order methods, where the inexactness is handled using a-posteriori error analysis. The Alexandra Schwartz presented numerical strategies are illustrated for the POD University of Würzburg and the Reduced-Basis method. Institute of Mathematics [email protected] Stefan Volkwein Universität Konstanz Jörg Franke [email protected] University of Dortmund (TU) Department of Economics MS75 [email protected] Computational Methods for Equilibrium: Making the Most of Optimization Christian Kanzow University of Wuerzburg Many phenomena are modeled as equilibrium problems [email protected] consisting of simultaneous optimization by multiple agents (MOPEC). In the case of Walrasian equilibrium, we con- Wolfgang Leininger sider solution methods that solve a sequence of optimiza- University of Dortmund (TU) tion subproblems for only one agent at a time. We show Department of Economics how to guide this sequence so that the algorithm converges. [email protected]

Jesse Holzer University of Wisconsin - Madison MS75 Madison, USA Convergence Analysis for Path-Following Methods [email protected] Applied to Optimal Control Problems Subject to An Elliptic Variational Inequality

MS75 In the talk, we consider the approximate solution of an op- Regularization Methods for Mathematical Pro- timal control problem subject to an elliptic variational in- grams with Complementarity Constraints equality. The resulting optimization problem is an infinite- dimensional MPCC. The problem is regularized in the fol- Mathematical programs with complementarity constraints lowing way: The variational inequality is replaced by a form a difficult class of optimization problems. Standard semilinear elliptic equation. Existence of solutions of the constraint qualifications are typically violated. Therefore, regularized problem is shown. Moreover, these solutions more specialized algorithms are applied. A popular method depend continuously and Frechet differentiably on the reg- is the regularization scheme by Scholtes. In the meantime, ularization parameter. Convergence of the regularized so- however, there exist a number of different regularization lutions to a solution of the original MPCC is proven to- approaches for the solution of MPCCs. Here we first give gether with convergence rates with respect to the regular- a survey of the existing methods, introduce a new one, ization parameter. and improve the existing convergence assumptions of most methods. Daniel Wachsmuth Johann Radon Institute for Computational and Applied Christian Kanzow Mathematics, Linz, Austria University of Wuerzburg [email protected] [email protected] Karl Kunisch Tim Hoheisel Karl-Franzens University Graz University of Würzburg Institute of Mathematics and Scientific Computing 97074 Würzburg, Germany [email protected] [email protected] Anton Schiela Alexandra Schwartz ZIB, Berlin University of Würzburg [email protected] Institute of Mathematics [email protected] MS76 Extended Formulations in Mixed-Integer Program- MS75 ming Effort Maximization in Asymmetric Contest Games with Heterogeneous Contestants – A Bilevel Several problems in the optimal planning of production Problem in Economy schedules can be formulated as mixed-integer programs. Extended formulations strengthen the original formulation We model the lobbying process between a politician and by adding further variables. We review several techniques lobbyists as a contest game where the politician can en- to construct extended formulations. We characterize cases courage or discourage specific lobbyists from participating. where the extended formulation provides the characteri- 152 OP11 Abstracts

zation of the convex hull of the feasible set in a higher MS77 dimensional space. We discuss cases where the projection Nonlinear Mpc in the Microsecond Range Us- of the extended formulation can explicitly computed. ing An Auto-Generated Real-Time Iteration Algo- rithm Michele Conforti Università degli Studi di Padova We present a strategy for automatic C-code generation of [email protected] real-time nonlinear model predictive control (MPC) algorithms, which are designed for applications with kilohertz sample rates. The corresponding software module for ex- MS76 porting the code has been implemented within the soft- Combinatorial Bounds on Nonnegative Rank and ware package ACADO Toolkit. Its symbolic representation Extended Formulations of optimal control problems allows to auto-generate optimized plain C-code. The exported code comprises a fixed In a breakthrough paper, Yannakakis (1991) proved that all step-size integrator that also generates the required sen- symmetric extended formulations of the perfect matching sitivity information as well as a real-time Gauss-Newton polytope have exponential size. Very little is known about method that is tailored for final production. Numerical general lower bounds the sizes of extended formulations. results show that the exported code has a promising com- We investigate a natural general lower bound, namely, the putational performance allowing to apply nonlinear MPC minimum number of combinatorial rectangles needed to to nontrivial processes at sampling times in the milli- and cover the support of the slack matrix of the polytope. microsecond range. Samuel Fiorini Joachim Ferreau Université Libre de Bruxelles K.U. Leuven sfi[email protected] [email protected]

Volker Kaibel, Kanstantsin Pashkovich, Dirk Theis Boris Houska Otto-von-Guericke Universität Magdeburg KU Leuven [email protected], [email protected], [email protected] [email protected] Moritz Diehl MS76 K.U.Leuven Symmetry of Extended Formulations for Matching- [email protected] Polytopes Yannakakis proved in 1991 that there are no symmet- MS77 ric polynomial size extended formulations for the perfect Solving Linear Complementarity Problems with matching polytopes of complete graphs. He furthermore Fast Numerical Methods conjectured that asymmetry cannot help to obtain polynomial size extensions for these polytopes. We prove that, In this talk we will show how to improve the speed of first however, the convex hulls of the characteristic vectors of order methods for solving linear complementarity problems matchings of logarithmic size in a complete graph do admit (LCPs). Specifically, we will concentrate on the numerical polynomial size non-symmetric extensions, while all sym- solution of LCPs that arise in CPU intensive applications metric extensions of these polytopes have super-polynomial such as rigid body dynamics and the pricing of American sizes. options. The methodology consists in interlacing first order iterations with subspace iterations on the free variables Volker Kaibel, Kanstantsin Pashkovich, Dirk Theis detected by the first order phase. The subspace phase con- Otto-von-Guericke Universität Magdeburg tributes to the resulting method in two aspects: a) the [email protected], [email protected], accurate identification of the active set; b) the speed of [email protected] convergence. Thus, the new method is able to compute very accurate solutions in less time than the original first order method. MS76 Tight Lower Bound on the Sizes of Symmetric Ex- Jose Luis Morales tensions of Permutahedra Departamento de Matematicas. ITAM. MEXICO. It is well known that the Birkhoff polytope provides a sym- [email protected] metric extended formulation of the permutahedron Πn of size Θ(n2). Recently, Goemans described asymptotically MS77 minimal extended formulation of Πn of size Θ(n log n). In this paper, we prove that Ω(n2) is a lower bound for A Distributed Newton Method for Network Utility the size of symmetric extended formulations of Πn.Thus, Maximization it is possible to determine tight lower bounds Ω(n2)and Ω(n log(n)) on the sizes of symmetric and non-symmetric Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) extended formulations of Πn . problems in a distributed manner, which suffer from slow Kanstantsin Pashkovich rate of convergence properties. This work develops an Otto-von-Guericke Universität Magdeburg alternative distributed Newton-type fast converging algo- [email protected] rithm for solving network utility maximization problems with self-concordant utility functions. By using novel matrix splitting techniques, both primal and dual updates for the Newton step can be computed using iterative schemes OP11 Abstracts 153

in a decentralized manner with limited information ex- of Atoms and Molecules change. We show that even when the Newton direction and the stepsize in our method are computed within some Determining the ground-state energy (lowest energy) of an error (due to finite truncation of the iterative schemes), electronic system (of an atom or a molecule) is the core the resulting objective function value still converges super- problem in quantum chemistry. Solving the SDP approxi- linearly to an explicitly characterized error neighborhood. mation of this problem is challenging since it requires par- Simulation results demonstrate significant convergence rate allel computation and high accuracy due to its excellent improvement of our algorithm relative to the existing sub- approximation values. We will present the computational gradient methods based on dual decomposition. results for the largest dense (Schur complement matrix) SDP solved so far, and further directions tackle this diffi- Asu Ozdaglar,ErminWei cult problem. MIT [email protected], [email protected] Mituhiro Fukuda Tokyo Institute of Technology Ali Jadbabaie Department of Mathematical and Computing Sciences Department of Electrical and Systems Engineering [email protected] University of Pennsylvania [email protected] Maho Nakata RIKEN [email protected] MS77 Mixed-Integer Nonlinear Real-Time Optimization Katsuki Fujisawa Department of Industrial and Systems Engineering We present work on nonlinear optimal control problems Chuo University in real time, where some control functions may only take [email protected] values from a discrete set. Examples are gear choices in transport, or on/off valves in engineering. Our approach is based on an Outer Convexification with respect to the inte- MS78 ger control functions, the direct multiple shooting method, Moment and SDP Relaxation Methods for Smooth and real-time iterations as first proposed by Diehl, Bock, Approximations of Nonlinear Differential Equa- and Schlöder. We discuss theoretical and numerical as- tions pects. Combining moment and semidefinite programming (SDP) Sebastian Sager relaxation techniques, we propose an approach to find Interdisciplinary Center for Scientific Computing smooth approximations for solutions of nonlinear differ- [email protected] ential equations. Given a system of differential equations, we apply a technique based on finite differences and sparse Christian Kirches SDP relaxations to obtain a discrete approximation of its Interdisciplinary Center for Scientific Computing solution. In a second step we apply maximum entropy esti- University of Heidelberg, Germany mation (using moments of a Borel measure associated with [email protected] the discrete approximation) to obtain a smooth closed-form approximation. MS78 Martin Mevissen On the Lasserre Hierarchy of Semidefinite Pro- LAAS-CNRS gramming Relaxations of Convex Polynomial Op- [email protected] timization Problems Jean Bernard Lasserre The Lasserre hierarchy of semidefinite programming ap- LAAS-CNRS proximations to convex polynomial optimization problems France is known to converge finitely under some assumptions. [email protected] [J.B. Lasserre. Convexity in semialgebraic geometry and polynomial optimization. SIAM J. Optim. 19, 1995–2014, Didier Henrion 2009.] We give a new proof of the finite convergence prop- LAAS-CNRS, University of Toulouse, & Faculty of erty, that does not require the assumption that the Hessian Electrical Engineering, Czech Technical University of the objective be positive definite on the entire feasible [email protected] set, but only at the optimal solution.

Etienne De Klerk MS78 Tilburg University [email protected] Ellipsoid-type Confidential Bounds on Semi- algebraic Sets via SDP Relaxation Monique Laurent In many applications, we want to know a confidential CWI, Amsterdam bound on semi-algebraic sets. For example, a sensor net- and Tilburg University work localization problem is to find a feasible point of semi- [email protected] algebraic sets. However, if its base network is not rigid, its sensor locations can not be fixed. Our method computes an ellipsoid-type confidential bound on semi-algebraic sets via MS78 SDP relaxation. This method can specify the possible re- SDP Approximation for the Electronic Structures gion of each sensor even when the network is not rigid. We also apply our method to polynomial optimization prob- 154 OP11 Abstracts

lems which have multiple optimal solutions and obtain a MS80 bound to cover all the optimal solutions. DIP with CHiPPS: Parallelizing Algorithms for Solving Integer Programs Makoto Yamashita Tokyo Institute of Technology Most practical algorithms for solving integer programs fol- Dept. of Mathematical and Computing Sciences low the basic paradigm of tree search. Such algorithms [email protected] are easy to parallelize in principle, but there are many challenges to achieving scalability in practice. We discuss Masakazu Kojima approaches to overcoming these challenges both using the Tokyo Institute of Technology course-grained parallelism afforded by parallelizing the tree [email protected] search itself and the fine-grained parallelism afforded by parallelizing the computations that take place in processing a single search tree node. MS80 SDPA Project: Solving Large-scale Semidefinite Ted Ralphs Programs Department of Industrial and Systems Engineering Lehigh University Solving extremely large-scale SDPs has a significant im- [email protected] portance for the current and future applications of SDPs. In 1995, we have started the SDPA Project aimed for solv- Matthew Galati, Yan Xu ing large-scale SDPs with numerical stability and accuracy. SAS Institute SDPA and SDPARA are pioneers’ code to solve general [email protected], [email protected] SDPs. In particular, it has been successfully applied on quantum chemistry, the SDPARA on a supercomputer has succeeded to solve the largest SDP and made a new world MS80 record. Solving Hard MIP Instances using Massively Par- allelized MIP Solvers Katsuki Fujisawa Department of Industrial and Systems Engineering We present parallel implementations of state-of-the-art Chuo University MIP solvers, CPLEX and SCIP, on a distributed mem- [email protected] ory computing environment. The implementations are constructed using a single software framework that enables us Makoto Yamashita to execute sequential branch-and-bound codes in parallel. Tokyo Institute of Technology We show computational results conducted with the paral- Dept. of Mathematical and Computing Sciences lel MIP solvers using up to 7,168 cores of HLRN II. These [email protected] results include the solutions to two open instances from MIPLIB2003 that had not been solved yet. Maho Nakata RIKEN Yuji Shinano [email protected] Zuse Institute Berlin Takustr. 7 14195 Berlin [email protected] Mituhiro Fukuda Tokyo Institute of Technology Department of Mathematical and Computing Sciences Tobias Achterberg [email protected] IBM Deutschland Research & Development GmbH [email protected]

MS80 Timo Berthold, Stefan Heinz Which Mixed Integer Programs could a Million Zuse Institute Berlin CPUs Solve? Takustr. 7 14195 Berlin [email protected], [email protected] There is a trend in supercomputing to employ evermore computing cores. Today, the current top 10 machines Thorsten Koch have on average 150000 cores and likely a million cores Zuse Institute Berlin will be available soon. The question arises how to harness [email protected] these vast computing capabilities to solve new classes of mixed integer programs. Based on our experiences with distributed parallel solvers we will systematically investi- MS81 gate under which conditions such a machine might eﬃ- A POD Approach to Robust Controls in PDE Op- ciently solve MIPs. timization

Thorsten Koch A strategy for the fast computation of robust controls of Zuse Institute Berlin PDE models with random-field coefficients is presented. A [email protected] robust control is defined as the control function that minimizes the expectation value of the objective over all co- Yuji Shinano efficient configurations. A straightforward application of Zuse Institute Berlin the adjoint method on this problem results in a very large Takustr. 7 14195 Berlin optimality system. In contrast, a fast method is presented [email protected] where the expectation value of the objective is minimized with respect to a reduced POD basis of the space of con- OP11 Abstracts 155

trols. Comparison of the POD scheme with the full opti- [email protected] mization procedure in the case of elliptic control problems with random reaction terms and with random diffusivity Volker Schulz demonstrates the superior computational performance of University of Trier the POD-based method. Department of Mathematics [email protected] Alfio Borzi Institute for Mathematics University of Würzburg MS81 alfi[email protected] Shape Optimization under Uncertainty from Stochastic Programming Point of View Gregory von Winckel University of Graz Shape optimization with linearized elasticity under Institute of Mathematics stochastic loading bears conceptual similarity with finite- [email protected] dimensional two-stage linear stochastic programming. Shapes correspond to nonanticipative first-stage decisions in the stochastic program. The weak formulation of the MS81 elasticity pde forms an analogue to the second-stage opti- Stochastic Collocation for Optimization Problems mization problem. Based on these observations, we present Governed by Stochastic Partial Differential Equa- risk-neutral and risk-averse stochastic shape optimization tions problems, discuss algorithms for their solution, and report computational results. Many optimization optimization problems in engineering and science are governed by partial differential equations Ruediger Schultz (PDEs) with uncertainties in the input data. Since the so- University of Duisburg-Essen lution of such PDEs is a random field and enters the objec- [email protected] tive function, the objective function usually involves statistical moments. Optimization problems governed by PDEs with uncertainties in the input data are posed as a par- MS82 ticular class of optimization problems in Bochner spaces. Optimization with Risk Via Stochastic Dominance This allows us to use the frameworks for derivative based Constraints optimization methods in Banach spaces. However numerical solution of these problems is more challenging than The theory of stochastic dominance provides tools to com- deterministic PDE constrained optimization problems, be- pare the distributions of two random variables. Notions cause it requires discretization of the PDE in space/time of stochastic dominance have been used in a wide range as well as in the random variables. We discuss stochas- of areas, from epidemiology to economics, as they allow tic collocation methods for the numerical solution of such for comparison of risks. Such concepts are also useful in optimization problems, explore the decoupling nature of an optimization setting, where they can be used as con- this method for gradient and Hessian computations as well straints to control for risk – an area that has gained atten- as preconditioning, and we present estimates for the dis- tion in the literature since its introduction by Dentcheva cretization error. and Ruszczynski in a 2003 paper. The use of stochastic dominance in a multivariate setting can then allow for Matthias Heinkenschloss multi-criterion risk comparisons, which is useful not only Rice University for optimization but also from a pure decision-making per- Dept of Comp and Applied Math spective. The multivariate setting, however, poses signif- [email protected] icant challenges, as even testing for such conditions may be difficult. In this talk we introduce some alternative Drew Kouri concepts based on the notion of multivariate linear dom- Department of Computational and Applied Mathematics inance, where linear combinations of the underlying ran- Rice University dom vectors are compared using coefficients from a certain [email protected] user-specified set that may represent the opinions of multiple decision makers. When the random vectors being compared have discrete distributions, these new stochas- MS81 tic dominance relationships can be represented by a finite Numerical Treatment of Uncertainties in Aerody- number of inequalities. Moreover, some of these concepts namic Shape Optimization can be parameterized in order to allow for a relaxation of the dominance condition. These results yield concrete con- In this talk, a novel approach towards stochastic dis- ditions can be checked, either as stand-alone comparisons tributed aleatory uncertainties for the specific application or as constraints in the optimization setting. We discuss of optimal aerodynamic design under uncertainties will be these formulations in detail and present some practical ex- presented. Proper robust formulations of the determin- amples to illustrate the ideas. istic problem as well as efficient adaptive discretization techniques combined with algorithmic approaches based on Tito Homem-de-Mello one-shot methods attacking the additional computational Northwestern University complexity will be discussed. Further, numerical results of [email protected] robust aerodynamic shape optimization under uncertain flight conditions as well as geometrical uncertainties will Sanjay Mehrotra be presented. IEMS Northwestern University Claudia Schillings [email protected] University of Trier, Germany 156 OP11 Abstracts

Jian Hu Southampton University Northwestern University [email protected] [email protected]

MS83 MS82 Convex Relaxation for the Clique and Clustering Scenario Generation in Stochastic Optimization Problems

Some approaches for generating scenarios in stochastic op- Given data with known pairwise similarities, partitioning timization are shortly reviewed. The Quasi-Monte Carlo the data into disjoint clusters is equivalent to partition- (QMC) approach is discussed in more detail. In partic- ing a particular graph into disjoint cliques. We consider ular, we provide conditions implying that QMC may be the related problem of identifying the maximum subgraph successfully applied to two-stage dynamic stochastic pro- comprised of k disjoint cliques of a given graph. We show grams and is superior to Monte Carlo. Some numerical that this NP-hard problem can be solved exactly by re- experience is also presented. laxing to a convex optimization problem by replacing rank with the nuclear norm for certain input graphs. Werner Roemisch Humboldt-University Berlin Brendan Ames Instititute of Mathematics University of Waterloo [email protected] [email protected]

Stephen A. Vavasis MS82 University of Waterloo Distributed Schemes for Computing Equilibria of Dept of Combinatorics & Optimization Monotone Nash Games [email protected] In this talk, we consider the distributed computation of equilibria arising in monotone Nash games over continu- MS83 ous strategy sets. Direct application of projection-based Convex Graph Invariants schemes are characterized by a key shortcoming: they can accommodate strongly monotone mappings only. We de- The structural properties of graphs are characterized in velop single-timescale regularized variants (via Tikhonov terms of invariants, which are functions of graphs that do and proximal-point methods) that can accommodate a not depend on node labeling. We discuss convex graph in- more general class of problems and provide convergence variants, which are graph invariants that are convex func- theory. Several extensions of this framework are stud- tions of the adjacency matrix of a graph. Some examples ied, including inexact projection schemes, partially coordi- include the maximum degree, the MAXCUT value (and nated generalizations (where players choose steplength se- its semidefinite relaxation), and spectral invariants such quences independently) and generalizations to the stochas- as the sum of the k largest eigenvalues. Such functions tic regime. can be used to construct convex sets that impose various structural constraints on graphs, and thus provide a unified Uday Shanbhag framework for solving several interesting graph problems Department of Industrial and Enterprise Systems via convex optimization. Engineering University of Illinois at Urbana-Champaign Venkat Chandrasekaran, Pablo A. Parrilo, Alan Willsky [email protected] Massachusetts Institute of Technology [email protected], [email protected], [email protected] MS82 Stochastic Mathematical Programs with Equilib- MS83 rium Constraints Nuclear Norm of Multilinear Forms and Tensor Rank In this talk, we discuss numerical approximation schemes for a two stage stochastic programming problem where We will define Schatten and Ky Fan norms for tensors of the second stage problem has a general nonlinear com- arbitrary order and discuss their basic properties. In par- plementarity constraint: first, the complementarity con- ticular, we show that the Schatten 1 norm is the convex straint is approximated by a parameterized system of in- envelope of tensor rank on the spectral norm unit ball – equalities with a well-known NLP regularization approach a generalization of a well-known result in matrix comple- in deterministic mathematical programs with equilibrium tion. We will then discuss how one may compute Schatten constraints; the distribution of the random variables of the norms of a tensor via semidefinite relaxation of a general- regularized two stage stochastic program is then approxi- ized moment problem. mated by a sequence of probability measures. By treating the approximation problems as a perturbation of the origi- Lek-Heng Lim nal (true) problem, we carry out a detailed stability analy- University of Chicago sis of the approximated problems including continuity and [email protected] local Lipschitz continuity of optimal value functions, and outer semicontinuity and continuity of the set of optimal solutions and stationary points. A particular focus is given MS83 to the case when the probability distribution is approxi- The Convex Geometry of Linear Inverse Problems mated by the empirical probability measure which is also known as sample average approximation. Building on the success of generalizing compressed sensing to matrix completion, we extend the catalog of structures Huifu Xu that can be recovered from partial information. We de- OP11 Abstracts 157

scribe algorithms to decompose signals into sums of atomic that one is interested in finding solutions at the finest level signals from a simple, not necessarily discrete, set. These of detail. MG/Opt uses calculations on coarser levels to ac- algorithms are derived in a convex optimization framework celerate the progress of the optimization on the finest level. that generalizes previous methods based on l1-norm and I discuss convergence results for MG/Opt, along with is- nuclear norm minimization. We discuss general recovery sues affecting performance. guarantees for our approach and several example applications. Stephen G. Nash George Mason University Benjamin Recht Systems Engineering & Operations Research Dept. University of Wisconsin – Madison [email protected] [email protected]

Venkat Chandrasekaran, Pablo A. Parrilo, Alan Willsky MS85 Massachusetts Institute of Technology Multilevel Optimization with Reduced Order Mod- [email protected], [email protected], [email protected] els for PDE-Constrained Problems We present an adaptive multilevel generalized SQP-method MS85 for optimal control problems governed by nonlinear PDEs Sparse Interpolatory Surrogate Models for Poten- with control constraints. During the optimization itera- tial Energy Surfaces tion the algorithm generates a hierarchy of adaptively re- ﬁned discretizations. The discretized problems are then In this presentation we describe recent results on manag- each approximated by an adaptively generated sequence ing interpolatory surrogate models for potential energy sur- of reduced order models. The adaptive reﬁnement strate- faces. The objectives are to avoid the use of an expensive gies are based on error estimators for the original and the simulator with an interpolatory approximation, keep the discretized PDE, adjoint PDE and a criticality measure. number of interpolatory nodes at a moderate level for prob- Numerical results are presented. lems of dimension up to ten, and perform well on cluster architectures. We will discuss the motivating application, J. Carsten Ziems the algorithmic issues, and our solutions. We will also re- Technische Universitaet Darmstadt port computational results [email protected]

Carl T. Kelley Stefan Ulbrich North Carolina State Univ Technische Universitaet Darmstadt Department of Mathematics Fachbereich Mathematik tim [email protected] [email protected]

David Mokrauer Dept of Mathematics MS86 NC State University Global Optimization Methods for the Identification [email protected] of Biochemical Networks Model building is a key task in systems biology. In this con- MS85 text, model identification often becomes a bottleneck due A Linearly-Constrained Augmented Lagrangian to limited amount and low quality of experimental data. Method for PDE-Constrained Optimization The discrimination among different model candidates faces similar challenges. This work revisits the problems of pa- In this talk, I describe a linearly-constrained augmented rameter estimation and the optimal experimental design Lagrangian method for solving PDE-constrained optimiza- as challenging non-linear (dynamic) optimization problems tion problems. This method computes two directions, a and shows, through some examples, how to handle this Newton direction to reduce the constraint violation and complexity by means of suitable global optimization tech- a reduced-space direction to improve the augmented La- niques. grangian merit function. The reduced-space direction is computed from a limited-memory quasi-Newton approxi- Eva Balsa-Canto mation to the reduced Hessian. This method requires a IIM-CSIC minimal amount of information from the user, yet obtains [email protected] good performance on our test problems. Julio R. Banga Todd Munson IIM-CSIC Argonne National Laboratory Vigo, Spain Mathematics and Computer Science Division [email protected] [email protected] MS86 MS85 Reverse Engineering of Gene Expression via Opti- Multigrid Methods for PDE-constrained Optimiza- mal Control tion Many cellular networks have evolved to maximize fit- MG/Opt is a multigrid optimization approach for the solu- ness. Experimental and numerical observations suggest tion of constrained optimization problems. The approach that gene onset in bacterial amino acid metabolism follows assumes that one has a hierarchy of models, ordered from a “just-in-time’ pattern that can be understood as the so- fine to coarse, of an underlying optimization problem, and lution of a dynamic optimization problem. Here we use 158 OP11 Abstracts

rigorous tools such as the Minimum principle and Linear- Quadratic Programs Quadratic optimization to reverse engineer genetic timing. Our analysis suggests new hypotheses about the general We study six families of unbounded convex sets that are validity of this design principle. associated with non-convex mixed-integer quadratic programs. The six cases arise by permitting the variables to Diego A. Oyarzun be either continuous, integer-constrained, or mixed, and by Department of Bioengineering specifying them to be either non-negative or free. It turns Imperial College London out that none of these convex sets are polyhedra. Never- [email protected] theless, we show that most of them have infinitely many facets. MS86 Samuel Burer Optimal Design of Transcription Networks University of Iowa Dept of Management Sciences The ongoing advance in synthetic biology allows for the [email protected] implementation of artificial biochemical networks with increasing complexity and accuracy. This calls for the use Adam N. Letchford of computational methods to cope with the design process Lancaster University Management School and avoid inefficient try and error approaches. Every sys- [email protected] tem is subject to random perturbations and uncertainties and trying to optimize the worst case performance leads to nonlinear semi-infinite min-max optimization problems MS87 which we solve by replacing them with a sequence of fi- Lower Bounds for the Chvtal-Gomory Closure in nite dimensional non linear programs. The method is il- the 0/1 Cube lustrated by optimizing and stabilizing the period of the circadian oscillator of Drosophila. Although well studied, important questions on the rank of the Chvtal-Gomory operator when restricting to polytopes Marcel Rehberg in the n-dimensional 0/1 cube have not been answered yet. Freiburg University, Germany In this paper we develop a simpler method to establish [email protected] lower bounds. We show the power and applicability of this method on classical examples as well as provide new Dominik Skanda families of polytopes with high rank. Furthermore, we pro- Department of Applied Mathematics vide a deterministic family of polytopes achieving a Chvtal- University of Freiburg, Germany Gomory rank of at least (1+1/e)n - 1 and we show how to [email protected] obtain a lower bound on the rank from solely examining the integrality gap. Dirk Lebiedz University of Freiburg Sebastian Pokutta Center for Systems Biology Massachusetts Institute of Technology [email protected] [email protected] Gautier Stauffer MS86 University of Bordeaux 1 Robustness Analysis of Biomolecular Networks via gautier.stauff[email protected] Polynomial Programming Dynamical models of biomolecular networks commonly MS87 contain significant parametric uncertainty, which affects The Stable Set Polytope of Claw-free Graphs : Ex- the model behaviour and the network’s related biological tended Formulations, Optimization and Separation function. The talk presents methods of polynomial programming which allow to quantify the effects of uncertain- In this talk, we show how recent algorithmic ideas for opti- ties on the model behaviour, and to compute a level of mizing over the stable polytope of claw-free graphs can be parametric uncertainty up to which no significant changes straightforwardly converted into an extended formulation in the qualitative model behaviour occur. In this way, the for this problem. We then explain how to exploit similar robustness analysis problem can be handled via a convex ideas to build another extended formulation from the very optimization approach. basic definition of the convex hull. Finally, building upon those results, we discuss how to derive a polytime sepa- Steffen Waldherr ration routine and retrieve the linear description in the Institute for Systems Theory and Automatic Control original space. Universität Stuttgart [email protected] Yuri Faenza Università degli Studi di Padova Frank Allgöwer yuri faenza ¡[email protected]¿ Institute for Systems Theory in Engineering University of Stuttgart Gianpaolo Oriolo [email protected] Università di Tor Vergata gianpaolo oriolo ¡[email protected]¿

MS87 Gautier Stauﬀer Convex Hulls for Non-convex Mixed Integer University of Bordeaux 1 gautier.stauﬀ[email protected] OP11 Abstracts 159

MS87 quadratic constraints. We consider eigenvalue based re- 2-clique-bond of Stable Set Polyhedra laxations, which are suitable for large scale problems. The weight redistribution idea allows to tighten these eigen- A 2-clique-bond is a generalization 2-clique-join where the value bounds. We present some preliminary computational subsets of nodes that are connected on each shore of the results which compare favourably with previous eigenvalue partition are two (not necessarily disjoint) cliques. We based relaxations. study the polyhedral properties of the stable set polytope of a graph G obtained as the 2-clique-bond of two graphs Franz Rendl G1 and G2. In particular, we prove that a linear descrip- Universitat Klagenfurt tion of the stable set polytope of G is obtained by properly Institut fur Mathematik composing the linear inequalities describing the stable set [email protected] polytopes of smaller graphs that are related to G1 and G2. Abdel Lisser Paolo Ventura Paris Orsay Istituto di Analisi dei Sistemi ed Informatica [email protected] [email protected] Mauro Piacentini MS88 La Sapienza, Roma [email protected] Semidefinite Code Bounds Based on Quadruple Distances MS88 Error correcting codes are stable sets in highly symmetric, but exponential sized graphs. Exploiting this symmetry Comparison of Bounds for Some Combinatorial allows to transform SDP bounds for the stability num- Optimization Problems ber into effective coding bounds. A striking example is In this talk we relate several semidefinite programming re- the Lovász theta bound, which yields a linear sized LP: laxations for the graph partition problem and the band- Delsarte’s bound. We present a stronger bound based on width problem in graphs, such as those of Donath- quadruples of code words. The feasible region of our SDP Hoffman, Karisch-Rendl, Wolkowicz-Zhao, Zhao-Karisch- consists of matrices indexed by pairs of words, that are in- Rendl-Wolkowicz. We also present new bounds for the variant under the symmetries of the Hamming cube. Using mentioned problems that are competitive with previously representation theory of the symmetric group, the invari- known ones. ant algebra can be block diagonalized, allowing the bound to be computed in polynomial time. Computationally, we Renata Sotirov obtain several improved bounds. In particular we find that Tilburg University the quadruply shortened Golay code is optimal. [email protected] Dion Gijswijt CWI, Amsterdam MS89 Leiden University A Two-Scale Approach for Optimization of Fine [email protected] Scale Geometry in Elastic Macroscopic Shapes We investigate macroscopic geometries with geometric de- MS88 tails located on a regular lattice. These details are sup- New SDP Relaxations of Stable Set Problems in posed to be parametrized via a finite number of parame- Hamming Graphs ters over which we optimize. Achieved results reveal phenomena on different length scales and reflect the multiscale We provide a new upper bound on the maximal size of nature of the optimization problem. Hence, we employ a the stable set in Hamming graphs via a new semidefinite two-scale approach based on boundary elements for the programming (SDP) relaxation. Our approach based on an elastic problem on the microscale and finite elements on SDP relaxation of the more general quadratic assignment the macroscale. Effective material properties will be stud- problem. We show how to exploit group symmetry in the ied and relations to laminate based optimization will be problem data and get a much smaller SDP problem in this investigated. special case. Benedict Geihe Marianna Nagy Rheinische Friedrich-Wilhelms-Universität Bonn Tilburg University, The Netherlands Institut für Numerische Simulation [email protected] [email protected] Etienne De Klerk, Renata Sotirov Tilburg University MS89 [email protected], [email protected] Shape Optimization with Stochastic Dominance Constraints MS88 Bringing together stochastic and shape optimization, we SDP Versus Eigenvalue Approaches to Bandwidth investigate elastic structures under random volume and and Partition Problems surface forces. Drawing on concepts from linear two-stage stochastic programming we formulate shape optimization Bandwidth and partition problems are in general NP models with stochastic dominance constraints. The latter complete. As combinatorial optimization problems they single out shapes, whose compliances compare favourably have natural formulations in binary variables involving with preselected benchmark random variables. In our algo- 160 OP11 Abstracts

rithms, shape variations arise from parametric shape des- the low-fidelity model is achieved by aligning the airfoil critions, leading to nonlinear programs in finite dimension. surface pressure distribution with that of the high-fidelity Illustrative computational results complete the talk. model using a shape-preserving response prediction technique. We present several numerical applications to airfoil Martin Pach design for both transonic and high-lift conditions. University of Duisburg-Essen Department of Mathematics Slawomir Koziel, Leifur Leifsson [email protected] Reykjavik University School of Science and Engineering [email protected], [email protected] MS89 On Certain and Uncertain Aerodynamic Shape Op- timization MS90 Optimal Control of Particles in Fluids Almost any technical process is prone to uncertainties with- ine the model describing this process. Aerodynamic shape We present techniques for optimizing particle dispersions optimization is one challenging example as part of this gen- flows and show the application spectrum, power and effi- eral problem class. We will highlight the challenges caused ciency of space mapping approaches that are based on a by uncertainties present in aerodynamics and shape opti- hierarchy of models ranging from a complex to a simple mization and also give ideas for the numerical treatment one. Space mapping allows for the easy and efficient treat- of these challenges. Numerical results achieved within col- ment of stochastic design problems. To control the random laborative efforts together with aircraft industry and the particle dynamics in a turbulent flow we suggest a Monte- German Aerospace center will be presented. Carlo aggressive space mapping algorithm that yields very convincing numerical results. Volker Schulz University of Trier Rene Pinnau Department of Mathematics Technische Universität Kaiserslautern [email protected] Fachbereich Mathematik [email protected] Stephan Schmidt University of Trier [email protected] MS90 Surrogate-Based Optimization for Marine Ecosys- Claudia Schillings tem Models University of Trier, Germany Understanding the oceanic CO2 uptake is of central impor- [email protected] tance for projections of climate change and oceanic ecosys- tems. The underlying models are governed by coupled sys- MS90 tems of nonlinear parabolic partial differential equations for ocean circulation and transport of biogeochemical trac- A Space Mapping Approach for the p-Laplace ers. The aim is to minimize the misfit between parameter Equation dependent model output and given data. Here we show Motivated by car safety applications the goal is to de- that using cheaper surrogate models significantly reduces termine a thickness coefficient in the nonlinear p-Laplace the optimization cost. equation. The associated structural optimization problem Malte Prie is hard to solve. Therefore, the computationally expensive, Christian-Albrechts-Universitaet Kiel nonlinear equation is replaced by a simpler, linear model. [email protected] A space mapping technique is utilized to link the linear and nonlinear equations and drives the optimization iteration of the nonlinear equation using the fast linear equation. Thomas Slawig Numerical examples illustrate the presented approach. Christian-Albrechts-Uni Kiel Department of Computer Science Oliver Lass [email protected] Universitaet Konstanz [email protected] Slawomir Koziel Reykjavik University Stefan Volkwein School of Science and Engineering Universität Konstanz [email protected] [email protected] PP1 MS90 Optimality Conditions and Duality in Nondifferen- Variable-fidelity Design Optimization of Airfoils us- tiable Multiobjective Programming ing Surrogate Modeling and Shape-preserving Re- sponse Prediction A nondifferentiable multiobjective problem is considered. Fritz John and Kuhn-Tucker type necessary and sufficient A computationally efficient methodology for airfoil design conditions are derived for a weak efficient solution. Kuhn- optimization is presented. Our approach exploits a cor- Tucker type necessary conditions are also obtained for a rected physics-based low-fidelity surrogate that replaces, properly efficient solution. Weak and strong duality theo- in the optimization process, an accurate but computation- rems are established for a Mond-Weir type dual. Moreover, ally expensive high-fidelity airfoil model. Correction of for a converse duality theorem we discuss a special case of OP11 Abstracts 161

nondiﬀerentiable multiobjective problem, where subgradi- signed, one did not even think of applying mathemati- ents can be computed explicitly. cal optimization one day, which results in various problems. We present a new model with desirable properties Izhar Ahmad for optimization, which is also capable of extensions to King Fahd University of Petroleum and Minerals optimization-based feedback and the inclusion of param- [email protected] eter estimation, and optimal solutions therefor.

Michael Engelhart PP1 Heidelberg University Adjoint-Based Full-Waveform Inversion for Param- Interdisciplinary Center for Scientiﬁc Computing (IWR) eter Identiﬁcation in Seismic Tomography [email protected]

We present a Newton-type method for full-waveform seis- Sebastian Sager mic inversion and propose a misfit criterion based on Interdisciplinary Center for Scientific Computing the convolution and the L2-distance of observed and sim- [email protected] ulated seismograms. The implementation features the adjoint-based computation of the gradient and Hessian- vector products of the reduced problem, a Krylov subspace Joachim Funke method to solve the Newton system in matrix-free fashion, Heidelberg University spatial discretization of the elastic wave equation by high- Department of Psychology order finite elements and parallelization with MPI. [email protected] Christian Boehm Technische Universitaet Muenchen PP1 [email protected] Solving Classification Problems by Approximate Minimal Enclosing Ball Algorithms

Michael Ulbrich Constructing classification models is, under certain hy- Technical University of Munich potheses, equivalent to the solution of a Minimal Enclos- Chair of Mathematical Optimization ing Ball (MEB) problem. Both tasks require the solution [email protected] of quadratic programming problems, which in many applications are large and not sparse. We analyze classical PP1 Support Vector Machine (SVM) methods and new algorithms that, exploiting the concept of -coreset to com- An Impulse Control Approach For Dike Height Op- pute approximate MEBs, can be fruitfully applied in the timization classification framework. Experimental results on several This paper determines the optimal timing as well as the benchmark datasets are reported. optimal level of dike updates to protect against floods. The Emanuele Frandi trade off is that a dike update (i.e. a dike height increase) Università degli Studi dell’Insubria is costly, but at the same time such an update reduces the Italy probability of a flood. In this paper we present the Impulse [email protected] Control approach as an alternative method to the Dynamic Programming approach used in Eijgenraam et al. (2010). Maria Grazia Gasparo Mohammed Chahim Università degli Studi di Firenze Dept. of Econometrics & Operations Research, CentER Italy Tilburg University mariagrazia.gasparo@unifi.it [email protected] Ricardo Nanculef˜ Ruud Brekelmans, Dick den Hertog Federico Santa Maria Technical University Dept. of Econometrics & Operations Research, CentER, Chile Tilburg University [email protected] [email protected], [email protected] Alessandra Papini Università degli Studi di Firenze Peter Kort Italy Dept. of Econometrics & Operations Research, CentER, alessandra.papini@unifi.it Tilburg University and Dept. of Economics, University of Antwerp PP1 [email protected] Efficient Simulation and Parameter Estimation for a Biologically Inspired Bipedal Robot

PP1 A multi-body systems dynamics model for a bipedal robot A New Test-Scenario for Optimization-Based Anal- whose legs are actuated by eight series-elastic structures ysis and Training of Human Decision Making approximating the main human leg muscle groups is developed allowing automated diﬀerentiation with respect to For computer-based test-scenarios in the domain of com- model parameters. Based on the dynamics model a tailored plex problem solving, the computation of optimal solutions direct multiple shooting approach is applied for estimation yields an objective indicator function of participants’ per- of unknown parameters based on measurements from well formance. However, when these scenarios have been de- 162 OP11 Abstracts

deﬁned independent experiments of the real robot. • The Moreau-Yosida regularized form and the proximal mapping associated with the rank function can Christian Reinl, Martin Friedmann, Dorian Scholz be explicitly calculated. Technische Universit¨at Darmstadt • ∈{ } ≥ [email protected], For k 0, 1,...,p and r 0,let [email protected], r Sk := {M ∈M ,\(R)| rank M≤∇and M∫√ ≤∇}. [email protected]

Oskar Von Stryk Then Department of Computer Science r co Sk = {M ∈M ,\(R)|M∫√ ≤∇and M∗ ≤∇}. Technische Universität Darmstadt [email protected] • The generalized subdifferentials of the rank function all coincide and the common value is a vector space PP1 of M ,\(R) Robust Optimization Problems with Sums of Max- ima of Linear Functions Le Hai Yen Ph.D Student The sum of maxima of linear functions plays an important [email protected] role in LP models for inventory management, supply chain management, regression models, tumour treatment, and many other practical problems. In the literature, often the Jean-Baptiste Hiriart-Urruty wrong robust counterpart is used. We present new methods University of Toulouse for dealing with the correct robust counterpart: France [email protected] max{i,j (ζ,x)}≤d ∀ζ ∈Z, j∈J i∈I PP1 where i,j is a bi-affine function. We apply our methods Selection of Securitization Baskets with Consider- to toy and practical problems, and indeed find that oftenly ation of Conditional Value-at-Risk and Expected used methods lead to inferior solutions. Returns

Bram Gorissen,DickHertog Financial institutes use structured products for transfer- Tilburg University ring risk (Conditional Value-at-Risk) arising from loan bas- Tilburg, The Netherlands kets. Arranging the basket for such transactions is a com- [email protected], [email protected] plex task often done with naive heuristics being far from optimal. The presented approach is based on MINLPs with various risk-return objectives. We compare different for- PP1 mulations which we transform into MILPs according to Geometry Optimization of Branched Sheet Metal Rockafellar and Uryasev. We give numerical examples us- Products ing a Merton’s type portfolio model and Monte-Carlo simulation with Glasserman’s Importance Sampling. We consider the geometry optimization of hydroformed branched sheet metal products which are produced using Matthias Heidrich the technology of linear flow splitting explored in the Col- Technische Universit laborative Research Center 666. We present the associated Fachbereich Mathematik problem for optimizing the stiffness of the structure with [email protected] 3D linear elasticity equations as constraints. Then an algorithm for solving this problem using exact constraints and Stefan Ulbrich a globalization strategy based on adaptive cubic regular- Technische Universitaet Darmstadt ization is presented. Numerical results for an example are Fachbereich Mathematik given. [email protected] Thea Göllner, Wolfgang Hess, Stefan Ulbrich TU Darmstadt PP1 [email protected], Sensitivity Analysis and Parameter Estimation [email protected], [email protected] Methods for Models of Complex Biological Pro- cesses

Mathematical models of complex biological processes re- PP1 quire numerical methods for quantitative analysis, where On Some Strange Properties in Rank Minimization sensitivity analysis and parameter estimation play a cru- Problems cial role. Especially interesting is reverse sensitivity analysis which allow to determine which model data have what Consider a rank minimization problem: inﬂuence on a selected model output and thus to identify model structures. P Minimize f(A):=rankofA ( ) ∈C We present sensitivity analysis and parameter estimation subject to A , methods for models of reaction-diﬀusion equations. The methods are successfully applied in modelling of Min- where C is a subset of M ,\(R). system oscillations in Escherichia coli. We state some strange results for problem (P). • Every admissible point in (P) is a local minimizer. Alexandra G. Herzog OP11 Abstracts 163

Dep. of Mathematics and Computer Science, Univ. of Department of Econometrics & Operations Research and Marburg CentER [email protected] Tilburg University [email protected] Jens Herwig, Tanja Binder, Max Nattermann Dep. of Mathematics and Computer Science, Sebastian Sager University of Marburg Interdisciplinary Center for Scientific Computing [email protected], [email protected] [email protected], [email protected] Andrea Seidl Institute for Mathematical Methods in Economics Ekaterina Kostina Vienna University of Technology Fachbereich Mathematik und Informatik [email protected] Philipps-Universitaet Marburg [email protected] PP1 Coupling Edges in Graph Cuts PP1 Alternating-Direction Optimization with Mas- We study a new graph cut problem, cooperative cut, where sively Parallel Trust-Regions for Partially Separa- the cost is a submodular function on sets of edges. The re- ble Non-Linear Objectives sulting coupling of edges allows novel applications, e.g., improving image segmentation by favoring congruous bound- Large inverse problems consisting of a separable fidelity aries. It also generalizes some recent models in computer term and non-separable regularization term(s) can be ad- vision. Such expressive power comes at the price of a lower dressed through the ADMM method. Recent methods bound on the approximation factor. However, we also show (like Chambolles) can address the regularization term. how to find good solutions with bounded approximation The fidelity minimization then becomes a large number factors. (sometimes millions) of low-dimensional independent subproblems. For vector-valued data, these sub-problems may Stefanie Jegelka themselves be multi-dimensional. When highly nonlinear, Max Planck for Biological Cybernetics these can be solved in lock-step parallel using damped trust [email protected] regions, which are particularly well suited for GPU implementation. Jeff Bilmes University of Washington Kevin M. Holt [email protected] Varian Medical Systems [email protected] PP1 The Integral Approximation Problem for Mixed- PP1 Integer Nonlinear Optimal Control Numerical Solution of a Conspicuous Consumption Model with Constant Control Delay We propose a decomposition approach for Mixed Inte- ger Nonlinear Optimal Control Problems (MIOCPs). The We derive optimal pricing strategies for conspicuous con- MIOCP is decomposed into a relaxed continuous one and a sumption products in recession periods. We investigate MILP to find values for integer control functions. We dis- a two-stage economic optimal control problem, including cuss the connection of optimal solutions to sum up round- uncertainty of the recession length and delay effects of the ing solutions, tailored Branch-and-Bound algorithms and pricing strategy. We propose a structure-exploiting direct Lagrangian relaxations. We provide an upper bound on method for optimal control, targeting uncertainties by sce- the distance between the optimal MIOCP objective and nario trees and control delays by slack control functions. the one found by our computationally efficient decomposi- Numerical results illustrate the validity of our approach tion approach. and show the impact of uncertainties and delay effects on optimal economic strategies. Michael Jung IWR Heidelberg Tony Huschto [email protected] Interdisciplinary Center for Scientific Computing, Heidelberg University Sebastian Sager [email protected] Interdisciplinary Center for Scientific Computing [email protected] Gustav Feichtinger Institute for Mathematical Methods in Economics Gerhard Reinelt Vienna University of Technology IWR, University of Heidelberg [email protected] [email protected]

Richard Hartl Department of Business Administration PP1 University of Vienna Decentralized Model-Predictive Control for Au- [email protected] tonomous Vehicles in Cooperative Missions

Peter Kort For a scenario from environmental monitoring, a decentral- 164 OP11 Abstracts

ized approach for optimal cooperative control of heteroge- PP1 neous multi-vehicle systems is investigated. It is demon- Graph Partitioning and Applications strated that using approximated motion dynamics and a model-predictive control method based on MILP, optimal Applications of graph partitioning problems abound in dif- control inputs can be computed in real-time. By employing ferent areas,among them in theoretical physics and in VLSI an adaptive sampling strategy, the hybrid control problem layout. In this poster, we introduce exact approaches for is linked to an identification problem for the estimation and solving graph partitioning problems together with results prediction of a dispersal process of airborne contaminants. for the applications. Juliane Kuhn Frauke Liers Simulation, Systems Optimization, and Robotics Group Institut für Informatik Department of Computer Science, TU Darmstadt Universität zu Köln [email protected] [email protected]

Oskar Von Stryk Department of Computer Science PP1 Technische Universität Darmstadt AFréchet Differentiability Result for Shape Opti- [email protected] mization with Instationary Navier-Stokes Flow We consider shape optimization problems where an object PP1 is exposed to instationary Navier-Stokes flow. Assuming the data are sufficiently smooth we show Fréchet differ- Optimal Deceleration of Rotation of a Symmetric 2,∞ Body with Internal Degrees of Freedom in a Resis- entiability of the velocity with respect to W domain tive Medium variations in 2D/3D. Here, the handling of the incompress- ibility condition and the low time regularity of the pressure The problem of time-optimal deceleration of rotation of play a crucial role in the analysis. Furthermore, we present dynamically symmetric body is studied. It is assumed that numerical results using an adjoint-based approach for cal- the body contains a cavity filled with viscous liquid and a culating the shape derivatives. mass connected to the body by coupling with square-low dissipation. Deceleration moment of viscous friction forces Florian Lindemann acts on the body. The optimal control law for deceleration Technische Universitaet Muenchen of rotation in the form of synthesis, the operation time and Germany the phase trajectories are determined. [email protected]

Dmytro D. Leshchenko Michael Ulbrich Odessa State Academy of Civil Engineering and Technical University of Munich Architecture Chair of Mathematical Optimization leshchenko [email protected] [email protected]

Leonid D. Akulenko Stefan Ulbrich Institute for Problems in Mechanics RAS Technische Universitaet Darmstadt [email protected] Fachbereich Mathematik [email protected] Yanina S. Zinkevich, Alla L. Rachinskaya Odessa State Academy of Civil Engineering and Christian Brandenburg Architecture TU Darmstadt [email protected], [email protected] Germany [email protected]

PP1 Low Multilinear Rank Tensor Decomposition Via PP1 Singular Value Thresholding Recursive Formulation of Limited Memory Vari- able Metric Methods We present a new numerical method for tensor dimensionality reduction. The method is based on the tensor trace We propose a new recursive matrix formulation of limited class norm which allows an optimization formulation for memory variable metric methods. This approach enables each tensor mode for ﬁnding the best low multilinear rank to approximate both the Hessian matrix and its inverse tensor approximation. By using singular value threshold- and can be used for an arbitrary update from the Broy- ing (SVT) technique, the method is implemented itera- den class. The new recursive formulation requires approxi- tively to obtain low rank factor in each mode. Some nu- mately 4mn multiplications and additions for the direction merical examples illustrate the eﬃciency and accuracy of determination. our method. Ladislav Luksan,JanVlcek Na Li Institute of Computer Science Clarkson University Academy of Sciences of the Czech Republic Dept. of Mathematics [email protected], [email protected] [email protected]

Carmeliza Navasca PP1 Clarkson University Recursive Formulation of Limited Memory Vari- [email protected] OP11 Abstracts 165

able Metric Methods Technische Universität Darmstadt [email protected] In this contribution, we propose a new recursive matrix formulation of limited memory variable metric methods. This approach can be used for an arbitrary update from the PP1 Broyden class (and some other updates) and also for the A Randomized Coordinate Descent Method for approximation of both the Hessian matrix and its inverse. Large-Scale Truss Topology Design The new recursive formulation requires approximately 4mn multiplications and additions per iteration, so it is compa- We develop a randomized coordinate descent method for rable with other efficient limited memory variable metric minimizing the sum of a smooth and a simple nonsmooth methods. Numerical experiments concerning Algorithm 1, separable convex function and prove that the method ob- proposed in this report, confirm its practical efficiency. tains an -accurate solution with probability at least 1 − ρ in at most O((n/)log(n/ρ)) iterations, where n is the di- Ladislav Luksan,JanVlcek mension of the problem. This simplifies, improves and ex- Institute of Computer Science tends recent results of Nesterov [2/2010]. It appears that Academy of Sciences of the Czech Republic the method is suitable for solving large-scale truss topology [email protected], [email protected] design problems.

Peter Richtarik, Martin Takac PP1 University of Edinburgh The Use of Influenza Vaccination Strategies When [email protected], [email protected] Supply Is Limited The 2009 A (H1N1) influenza pandemic was rather atypi- PP1 cal. The world’s limited capacity to produce an adequate Piecewise Monotonic Regression Algorithm for vaccine supply over just a few months resulted in the de- Problems Comprising Seasonal and Monotonic velopment of public health policies that “had” to optimize Trends the utilization of limited vaccine supplies. We use optimal control theory to explore the impact of some of the con- In this research piecewise monotonic models for problems straints faced by most nations in implementing a public comprising seasonal cycles and monotonic trends are con- health policy that tried to meet the challenges that come sidered. In contrast to the conventional piecewise mono- from having access only to a limited vaccine supply that is tonic regression algorithms, our approach can efficiently never 100% effective. exploit a priori information about temporal patterns. It is based on reducing these problems to monotonic regres- Romarie Morales sion problems defined on partially ordered data sets. The Arizona State University latter are large-scale convex quadratic programming prob- [email protected] lems. They are efficiently solved by the GPAV algorithm.

Sunmi Lee Mathematical, Computational and Modeling Sciences Amirhossein Sadoghi Center, Department of Computer Science Arizona State University, Link¨oping University [email protected] [email protected]

Carlos Castillo Chavez Oleg Burdakov Arizona State University Linkoping University [email protected] [email protected]

Anders Grimvall PP1 Department of Computer Science Dynamic Modeling and Optimal Control for Indus- Link¨oping University,Sweden trial Robots in Milling Applications [email protected]

The application of industrial robots for milling tasks results in high process forces at the end effector which lead to path PP1 deviations caused by joint elasticities. A coupled simula- An Infeasible-Point Subgradient Method Using tion model of robot dynamics and its interaction with the Approximate Projections milling process is based on an extended rigid multi-body description incorporating joint elasticities and tilting ef- We introduce a subgradient algorithm which applies inex- fects. The implementation of automatic differentiation en- act projections and thus is not required to maintain feasi- ables computation of compensation trajectories by direct bility of the iterates throughout the algorithmic progress. optimal control methods. We prove its convergence under reasonable conditions, investigating two classical step size schemes. We also Christian Reinl, Martin Friedmann, Elmar Brendel present computational results from an application to 1- Technische Universität Darmstadt minimization (Basis Pursuit) as commonly considered in [email protected], compressed sensing. Here, projection inaccuracies are [email protected], caused by a truncated CG method which is applied to solve [email protected] the projection subproblems.

Oskar Von Stryk Andreas M. Tillmann Department of Computer Science Technische Universit¨at Braunschweig 166 OP11 Abstracts

[email protected]

Dirk Lorenz, Marc Pfetsch TU Braunschweig [email protected], [email protected]

PP1 Robust Markov Decision Processes

Markov decision processes (MDPs) are powerful tools for decision making in uncertain dynamic environments. How- ever, the solutions of MDPs are of limited practical use due to their sensitivity to distributional model parameters, which are typically unknown and have to be estimated by the decision maker. To counter the detrimental effects of estimation errors, we consider robust MDPs that offer probabilistic guarantees in view of the unknown parameters. To this end, we assume that an observation history of the MDP is available. Based on this history, we derive a confidence region that contains the unknown parameters with a pre-specified probability 1 − β. Afterwards, we determine a policy that attains the highest worst-case performance over this confidence region. By construction, this policy achieves or exceeds its worst-case performance with a confidence of at least 1 − β. Our method involves the solution of tractable conic programs of moderate size. Wolfram Wiesemann Department of Computing Imperial College London [email protected]

Daniel Kuhn, Berc Rustem Imperial College London [email protected], [email protected]

PP1 Robust Optimization Using Historical Data

We provide a robust solution approach for linear optimization problems with uncertain parameters. Only historical data on the uncertain parameters is used in order to construct the uncertainty set. The aim is to ﬁnd the tightest uncertainty set such that the constraints of the problem are satisﬁed with at least a given probability. This approach yields tighter uncertainty regions than the standard approach, and moreover does not require independency of the uncertain parameters. Ihsan Yanikoglu Department of Econometrics and OR, Tilburg University [email protected]

Dick den Hertog University of Tilburg The Netherlands [email protected]

Goos Kant Tilburg University [email protected]