Computational Optimisation Group

Seminar: Alternating Maximization: Unifying Framework for 8 Sparse PCA Formulations
2013-05-16 14:00 UTC
Title: Alternating Maximization: Unifying Framework for 8 Sparse PCA FormulationsSpeaker: Dr. Selin AhipasaogluAffiliation: Singapore University of Technology and DesignLocation: CPSE seminar room (C615 Roderic Hill)Time: 2:00pm
Abstract. Given a multivariate data set, sparse principal component analysis (SPCA) aims to extract several linear combinations of the variables that together explain the variance in the data as much as possible, while controlling the number of nonzero loadings in these combinations. In this paper we consider 8 different optimization formulations for computing a single sparse loading vector; these are obtained by combining the following factors: we employ two norms for measuring variance (L2, L1) and two sparsity-inducing norms (L0, L1), which are used in two different ways (constraint, penalty). Three of our formulations, notably the one with L0 constraint and L1 variance, have not been considered in the literature. We give a unifying reformulation which we propose to solve via a natural alternating maximization (AM) method. Besides this, we provide a package which contains implementations for various parallel architectures and briefly discuss how these algorithms can be used to achieve better object recognition in challenging data sets.
About the speaker. Selin Damla Ahipasaoglu is an Assistant Professor at the Singapore University of Technology and Design. She received her PhD in 2009 from Cornell University and specialises in developing algorithms for large scale optimization problems, in particular first-order methods for convex problems and applications in image processing. She held research positions at Princeton University and London School of Economics before joining SUTD. She is also a very keen teacher and an advocate of active and innovative classroom teaching for undergraduates.

Seminar: Hard-to-Solve Bimatrix Games
2013-05-22 14:00
Title: Hard-to-Solve Bimatrix GamesSpeaker: Prof. Bernhard von StengelAffiliation: Depatment of Mathematics – London School of Economics and Political ScienceLocation: CPSE seminar room (C615 Roderic Hill)Time: 2:00pm
Abstract. A bimatrix game is a two-player game in strategic form, a basic model in game theory. A Nash equilibrium is a pair of (possibly randomized) strategies, one for each player, so that no player can do better by unilaterally changing his or her strategy. In this talk, which will introduce the main concepts and geometric tools, we show that the commonly used Lemke-Howson algorithm for finding one equilibrium of a bimatrix game is exponential. The algorithm is a pivoting method similar to the simplex algorithm for linear programming. We present a class of square bimatrix games for which the shortest Lemke-Howson path grows exponentially in the dimension d of the game. We construct the games using pairs of dual cyclic polytopes with 2d facets in d-space. The paths are recursively composed so that their lengths grow like Fibonacci numbers. We also mention subsequent results and open problems in the area.
About the speaker. Diploma in Mathematics from Aachen, MSc in Computer Sciences at Austin/Texas (student of Edsger W. Dijkstra), PhD in Passau, Habilitation in Munich, Postdoc at Berkeley, Tilburg and ETH Zurich (with a Heisenberg grant), at LSE Mathematics since 1998. Interested in algorithmic game theory longer than the research area has that name.

Seminar: CVaR Approximations for Minimax and Robust Convex Optimization
2013-05-28 14:00
Title: CVaR Approximations for Minimax and Robust Convex OptimizationSpeaker: Prof. Huifu XuAffiliation: School of Engineering and Mathematical Sciences at City University of LondonLocation: Room 218 Huxley BuildingTime: 2:00pm
Abstract. Conditional value at risk (CVaR) has been widely used as a risk measure in finance. In this work, we propose to randomize decision variables of a deterministic parametric maximization problem and approximate the optimal (maximum) value by the CVaR of the randomized function. One of the main advantages of this approach is that computing CVaR is down to solving a one dimensional convex optimization problem even when the original problem is multi-dimensional and nonconvex. We apply the approximation scheme to a minimax (robust) optimization problem and a convex optimization problem with semi-infinite constraints indexed by uncertain parameters. In the latter application we use CVaR to approximate the semi-infinite constraint and then apply the Monte Carlo sampling method to discretize the CVaR approximated constraint. This approach is closely related to a popular randomization approach proposed by Calafiore and Campi where the continuum of uncertainty parameters is discretized through sampling. Error bounds for the optimal solutions of the approximate problems are derived under some moderate conditions and some numerical test results are reported. The proposed methods can be applied to distributional optimization where the distribution set is constructed through moments.
About the speaker. Huifu Xu is a Professor of Operational Research in the School of Engineering and Mathematical Sciences at City University of London. Before joining City University, he was a Senior Lecturer of Operational Research in the School of Mathematics at the University of Southampton. His expertise is in continuous optimization and operational research, including developing numerical methods and underlying theory for continuous optimization problems, particularly those involving uncertain data and/or equilibrium constraints. Over the past ten years, he has been actively working on stochastic mathematical programs with equilibrium problems and is recently developing interest in robust approaches for stochastic optimization and equilibrium problems. Huifu has published about 60 papers most of which are in the international journals of optimization and operational research.

Seminar: Distributionally robust control of constrained stochastic systems
2013-06-14 14:00
Title: Distributionally robust control of constrained stochastic systemsSpeaker: Bart Van ParysAffiliation: Automatic Control Laboratory at Swiss Federal Institute of TechnologyLocation: Room 217-218 Huxley BuildingTime: 2:00pm
Abstract. We investigate the control of constrained stochastic linear systems when faced with limited information regarding the disturbance process, that is, when only the first and second-order moments of the disturbance distribution are known. We employ two types of soft constraints to prevent the state from falling outside a prescribed target domain: distributionally robust chance constraints require the state to remain within the target domain with a given high probability, while distributionally robust conditional value-at-risk constraints impose an upper bound on the state’s expected distance to the target domain conditional on that distance being positive. The attribute 'distributionally robust' reflects the requirement that the constraints must hold for all disturbance distributions sharing the known moments. We argue that the design of controllers for systems accommodating these types of constraints is both computationally tractable and practically meaningful for both finite and infinite horizon problems. The proposed methods are illustrated in the context of a wind turbine blade control design case study where flexibility issues play an important role and for which the distributionally robust constraints make sensible design objectives.
About the speaker. Bart holds a BA degree in electrical engineering, and a MA degree in applied/engineering mathematics, both from the University of Leuven. Since September 2011 he has been a PhD student in the Swiss Federal Institute of Technology (ETH Zürich) under the supervision of Prof. Manfred Morari and Dr. Paul Goulart.

Seminar: Performance-based regularization in mean-CVaR portfolio optimization
2013-06-19 14:00
Title: Performance-based regularization in mean-CVaR portfolio optimizationSpeaker: Prof. Gah-Yi VahnAffiliation: Management Science and Operations – London Business SchoolLocation: Room 145 HuxleyTime: 2:00pm
Abstract. Regularization is a technique widely used to improve the stability of solutions to statistical problems. We propose a new regularization concept, performance-based regularization (PBR), for data-driven stochastic optimization. The goal is to improve upon Sample Average Approximation (SAA) in finite-sample performance while maintaining minimal assumptions about the data. We apply PBR to mean-CVaR portfolio optimization, where we penalize portfolios with large variability in the constraint and objective estimations, which effectively constrains the probabilities that the estimations deviate from the respective true values. This results in a combinatorial optimization problem, but we prove its convex relaxation is tight. We show via simulations that PBR substantially improves upon SAA in finite-sample performance for three different population models of stock returns. We also prove that PBR is asymptotically optimal, and further derive its first-order behavior by extending asymptotic analysis of M-estimators. This is joint work with Noureddine El Karoui (UC Berkeley Statistics) and Andrew EB Lim (NUS Business School)
About the speaker. Gah-Yi Vahn is an Assistant Professor of Management Science and Operations at London Business School. She has a BSc (1st Class Hons. with Univ. Medal) from the University of Sydney (2007), an MA in Statistics (2011) and a PhD in Operations Research (2012) from the University of California, Berkeley. Gah-Yi’s research interest is data-driven decision-making, in particular optimization with complex, high dimensional, and/or highly uncertain data, with applications to finance and operations management.

Seminar: Parallel block coordinate descent methods for huge-scale partially separable problems
2013-06-20 14:00
Title: Parallel block coordinate descent methods for huge-scale partially separable problemsSpeaker: Martin TakacAffiliation: School of Mathematics – University of EdinburghLocation: CPSE Seminar roomTime: 2:00pm
Abstract. In this work we show that randomized block coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially block separable smooth convex function and a simple block separable convex function. We give a generic algorithm and several variants thereof based on the way parallelization is performed. In all cases we prove iteration complexity results, i.e., we give bounds on the number of iterations sufficient to approximately solve the problem with high probability. Our results generalize the intuitive observation that in the separable case the theoretical speedup caused by parallelization must be equal to the number of processors. We show that the speedup increases with the number of processors and with the degree of partial separability of the smooth component of the objective function. Our analysis also works in the mode when the number of blocks being updated at each iteration is random, which allows for modelling situations with variable (busy or unreliable) number of processors. We conclude with some encouraging computational results applied to huge-scale LASSO and sparse SVM instances. This is a joint work with Dr. Peter Richtarik, University of Edinburgh.
About the speaker.

Seminar: Robust Data-Driven Approach in Decision Making Under Uncertainty
2013-06-20 16:00
Title: Robust Data-Driven Approach in Decision Making Under UncertaintySpeaker: Grani Adiwena HanasusantoAffiliation: Department of Computing – Imperial College LondonLocation: Room 301 William PenneyTime: 4:00pm
Abstract. We investigate robust data-driven approach in stochastic optimization problems where partial knowledge on the exogenous uncertainties is available to the decision maker. In contrast to the traditional model-based approach, a data-driven approach requires no assumptions on the underlying distribution of exogenous uncertainties. Estimation of conditional expectation is achieved using kernel regression scheme which evaluates the cost function solely at historical observations. If sparse historical observations are available, however, the estimation is inaccurate and the resulting decision performs poorly in out-of-sample tests. To alleviate this unfavourable outcome, we ‘robustify’ the decision against estimation errors by utilizing techniques from robust optimization. We show that the arising min-max problem can be reformulated as a tractable conic program. We further extend the proposed approach to multi-period settings and introduce an approximate dynamic programming framework that retains the tractability of the formulation and that is amenable to efficient parallel implementation. The proposed approach is tested across several application domains and is shown to outperform various non-robust schemes in terms of standard statistical benchmarks.
About the speaker. Grani Hanasusanto is a PhD student at the Department of Computing, Imperial College London, under the supervision of Dr. Daniel Kuhn. He obtained the BEng (Hons) degree in Electrical and Electronic Engineering from Nanyang Technological University, Singapore, and the MSc degree in Financial Engineering from National University of Singapore. His research interests are in numerical and computational methods and their applications.

Seminar: Interdiction Games on Markovian PERT Networks
2013-07-03 15:00
Title: Interdiction Games on Markovian PERT NetworksSpeaker: Eli GutinAffiliation: School of Industrial and Systems Engineering – Georgia Institute of TechnologyLocation: Room 218 Huxley BuildingTime: 3:00pm
Abstract. In a stochastic interdiction game a proliferator aims to minimize the expected duration of a nuclear weapons development project, while an interdictor endeavors to maximize the project duration by delaying some of the project tasks. We formulate static and dynamic versions of the interdictor’s decision problem where the interdiction plan is either pre-committed or adapts to new information revealed over time, respectively. The static model gives rise to a stochastic program, while the dynamic model is formalized as a multiple optimal stopping problem in continuous time and with decision-d ependent information. Under a Markov assumption, we prove that the static model reduces to a mixed-integer linear program, while the dynamic model reduces to a finite Markov decision process in discrete time that can be solved via efficient value iteration. We then generalize the dynamic model to account for uncertainty in the outcomes of the interdiction actions. We also discuss a crashing game where the proliferator can use limited resources to expedite tasks so as to counterbalance the interdictor’s efforts. The resulting problem can be formulated as a robust Markov decision process.
About the speaker. Eli Gutin completed his MEng in Computing at Imperial College in 2012. His prize-winning final year project on “Interdiction Games on Markovian PERT networks” was supervised by Daniel Kuhn & Wolfram Wiesemann. A year later, it was submitted for publication and is the subject of today’s talk.

Seminar: Risk neutral and risk averse approaches to multistage stochastic programming with applications to hydrothermal operation planning problems
2013-08-08 14:00
Title: Risk neutral and risk averse approaches to multistage stochastic programming with applications to hydrothermal operation planning problemsSpeaker: Dr. Wajdi TekayaAffiliation: Decision Trees GmbHLocation: Room 217 Huxley BuildingTime: 2:00pm
Abstract. This talk gives an overview of risk neutral and risk averse approaches to multistage stochastic programming with applications to hydrothermal operation planning problems. In the first part of this talk, we discuss risk neutral and risk averse approaches using coherent risk measures to multistage (linear) stochastic programming problems based on the Stochastic Dual Dynamic Programming (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system.In the second part of this talk, we discuss multistage programming with the data process subject to uncertainty. We consider a situation where the data process can be naturally separated into two components, one can be modeled as a random process, with a specified probability distribution, and the other one can be treated from a robust (worst-case) point of view. We formulate this in a time consistent way and derive the corresponding dynamic programming equations. In order to solve the obtained multistage problem we develop a variant of the (SDDP) method. We give a general description of the algorithm and present computational studies related to planning of the Brazilian interconnected power system.
About the speaker. Wajdi Tekaya is currently an HPCfinance postdoctoral fellow at Cambridge Systems Associates. He obtained his B.S. in industrial engineering from Tunisia Polytechnic School, M.S. in Operations Research from Paris IX University, Georgia Institute of Technology and Ph.D. in Operations Research from Georgia Institute of technology. His research interests are in computational approaches to stochastic programming with applications in energy and finance.

Seminar: Managing with Incomplete Inventory Information
2013-08-12 14:00
Title: Managing with Incomplete Inventory Information Speaker: Prof. Suresh P. SethiAffiliation: Center for Intelligent Supply Networks – University of Texas at DallasLocation: Room 217-218 Huxley BuildingTime: 2:00pm
Abstract. A critical assumption in the vast literature on inventory management has been that the current level of inventory is known to the decision maker. Some of the most celebrated results such as the optimality of base-stock policies have been obtained under this assumption. Yet it is often the case in practice that the decision makers have incomplete or partial information about their inventory levels. The reasons for this are many: Inventory records or cash register information differ from actual inventory because of a variety of factors including transaction errors, theft, spoilage, misplacement, unobserved lost demands, and information delays. As a result, what are usually observed are some events or surrogate measures, called signals, related to the inventory level. These relationships can provide the distribution of current inventory levels. Therefore, the system state in the inventory control problems is not the current inventory level, but rather its distribution given the observed signals. Thus, the analysis for finding optimal production or ordering policies takes place generally in the space of probability distributions. The purpose of this talk is to review recent developments in the analysis of inventory management problems with incomplete information.
About the speaker. Suresh P. Sethi is Eugene McDermott Professor of Operations Management and Director of the Center for Intelligent Supply Networks at The University of Texas at Dallas. He has written 7 books and published nearly 400 research papers in the fields of manufacturing and operations management, finance and economics, marketing, and optimization theory. He teaches a course on optimal control theory/applications and organizes a seminar series on operations management topics. He initiated and developed the doctoral programs in operations management at both University of Texas at Dallas and University of Toronto. He serves on the editorial boards of several journals including Production and Operations Management and SIAM Journal on Control and Optimization. He was named a Fellow of The Royal Society of Canada in 1994. Two conferences were organized and two books edited in his honor in 2005-6. Other honors include: IEEE Fellow (2001), INFORMS Fellow (2003), AAAS Fellow (2003), POMS Fellow (2005), IITB Distinguished Alum (2008), SIAM Fellow (2009), POMS President (2012).

Seminar: Added value of scenario tree based stochastic optimization in long and medium term planning of hydro power systems
2013-08-22 11:00
Title: Added value of scenario tree based stochastic optimization in long and medium term planning of hydro power systemsSpeaker: Dr. Georg OstermaierAffiliation: Location: Room 217 Huxley BuildingTime: 11:00am
Abstract. The changes in the dynamics of power prices in Germany within the last few years have implied significant decreases of revenues of pumped storage hydro systems. The earnings from daily peak/offpeak price spreads have declined whereby at the same time long term management of large reservoirs has become even more difficult due hardly predictable power price and inflow evolutions. Stochastic Optimization has been applied for hydro system management for a long time already, but only recently operators expect additional benefits given the changed and even more uncertain power market situation. Besides stochastic dual dynamic programming, scenario tree based methods are meanwhile applied, which so far have hardly been used for complex hydro systems due to the curse of dimensionality in stochastic programming. We apply efficient discretization methods for the generation of multi-dimensional scenario trees of power prices and inflows, based on moment matching and multinomial distributions. Furthermore, by using increased hardware efficiency it is meanwhile possible to set up and solve scenario tree based stochastic optimization models for even complex pumped storage systems. Ex post analyses have shown that outperformance over deterministic optimization in the range of 1-5 percent is achievable.
About the speaker. Georg Ostermaier is founder, owner and managing director of Decision Trees GmbH, a Munich based firm focussing on the practical application of mathematical and stochastic programming in the European Energy industry. Georg received his graduate degree in Electrical Engineering from the Technical University of Munich and his PhD in Operations Research from the University of St.Gallen, Switerland. Since 2006 he and his team have been developing stochastic optimization software systems for thermal power generation portfolios, hydro power generation systems, gas storage and gas contract valuation and gas procurment portfolio optimisation. Decision Trees GmbH has today a solid customer base in Germany, Austria, Switzerland, Norway and the United Kingdom and has proven to contribute to enhanced profits for energy producers in practice through stochastic optimization.

Seminar: Risk measures and time consistency
2013-09-26 14:00
Title: Risk measures and time consistencySpeaker: Prof. Alexander ShapiroAffiliation: School of Industrial and Systems Engineering – Georgia Institute of TechnologyLocation: Room 145 Huxley BuildingTime: 2:00pm
Abstract. In this talk we discuss basic theory of risk measures and risk averse optimization. Starting with the pioneering paper by Artzner et al, “Coherent measures of risk” (1999), this theory went through rapid development in recent years. We pay a special attention to a multistage setting, and, in particular, discuss the involved concepts of time consistency.
About the speaker. Alexander Shapiro is a Professor in the School of Industrial and Systems Engineering at Georgia Institute of Technology. He has published more than 120 research articles in peer reviewed journals and is a coauthor of several books (see below). His research is widely cited and he was listed as an ISI Highly Cited Researcher in 2004 (ISI = Institute for Scientic Information), links to his research ID: http://www2.isye.gatech.edu/~ashapiro/research.html. He is on the editorial board of several professional journals, such as Mathematics of Operations Research, ESAIM: Control, Optimization and Calculus of Variations, Computational Management Science. He was an area editor (Optimization) of Operations Research, currently he is the Editor-in Chief of the Mathematical Programming journal. He gave numerous invited keynote and plenary talks, including invited section talk (section Control Theory & Optimization) at the International Congress of Mathematicians 2010, Hyderabad, India http://www.icm2010.in/scientific-program/invited-speakers. Published Books: 1. Rubinstein, R.Y. and Shapiro, A., Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method, John Wiley and Sons, New York, 1993. 2. Bonnans, J. F. and Shapiro, A., Perturbation Analysis of Optimization Problems, Springer, New York, 2000. 3. Handbook on Stochastic Programming, edited by: A. Ruszczynski and A. Shapiro, North-Holland Publishing Company, Amsterdam, 2003. 4. Shapiro, A., Dentcheva, D. and Ruszczynski, A., Lectures on Stochastic Programming: Modeling and Theory , SIAM, Philadelphia, 2009.

Seminar: Numerical Aggregation of Trust Evidence: Its Analysis and Optimisation
2014-01-15 15:15
Title: Numerical Aggregation of Trust Evidence: Its Analysis and OptimisationSpeaker: Prof. Michael Huth and Dr. Jim Huan-Pu KuoAffiliation: Department of Computing – Imperial College LondonLocation: Room 217 Huxley BuildingTime: 3:15pm
Abstract. We have designed a language in which modellers can specify trust and distrust signals that, in their presence, generate a numerical score, and where such scores can be combined with aggregation operators to express risk postures for trust-mediated interactions in IT systems. Signals may stem from heterogenous sources such as geographical information, reputation, and threat levels. Aggregated scores then inform decisions by generating conditions that compare scores to threshold values of trustworthiness. We developed a generic approach to analysing such conditions by automatically converting them into code for the Satisfiability Modulo Theory solver Z3 from Microsoft Research. This allows us to automatically analyse, e.g., whether a condition is sensitive to the increase of a trustworthiness threshold by a specified amount. We would now like to understand better whether such analysis questions can be expressed in known models as used in optimisation. For example, let a condition say that the aggregated trust score has to be above 0.5. Solvers such as Z3 seem to be unable to compute the largest interval containing 0.5 such that all values of that interval could be chosen as trustworthiness threshold without changing the behaviour of the condition. On the other hand, Z3 is perfect for reflecting logical dependencies or inconsistencies between (dis)trust signals that occur in such conditions and are quantifier-free formulas of first-order logic. A prototype implementation of the tool is available at http://delight.doc.ic.ac.uk:55555
About the speaker.

Seminar: Revolutionizing Airline Planning & Scheduling with the Invention of Unified Optimization
2014-01-28 14:00
Title: Revolutionizing Airline Planning & Scheduling with the Invention of Unified OptimizationSpeaker: Dr. Nikolaos PapadakosAffiliation: Decisal LtdLocation: Room 345 Huxley BuildingTime: 2:00pm
Abstract. Airline planning and scheduling are complex mixed integer problems. To reduce complexity each of them has traditionally been split into stages. For example, scheduling is split into fleet assignment, aircraft scheduling, and crew scheduling, which are solved sequentially one after the other. These stages are, however, interdependent and airlines have to deal with under-optimal results and constraint violations. Decisal is the company that invented algorithms for Unified Optimization of these stages, greatly improving profit optimization and constraint satisfaction. The methodology for Unified Optimization includes several advancements of Benders Decomposition. Finally, in some cases, both the Benders master problem and the Benders subproblem are made of improved column generation algorithms.
About the speaker. Dr Nikos (Nikolaos) Papadakos is the research and development director of Decisal. Prior to that he worked as a research associate at Imperial College London where he also received a PhD in operations research and an MSc in advanced computing. He also holds a BSc in mathematics from the University of Athens. Finally, his work experience includes the Bank of Attica and Biomex Epe, in software development, sales, and customer support.

Seminar: Multi-stage Decision Optimization under Uncertainty
2014-03-21 14:00
Title: Multi-stage Decision Optimization under Uncertainty Speaker: Dr. Ronald HochreiterAffiliation: WU Vienna University of Economics and BusinessLocation: Room 218 Huxley BuildingTime: 2:00pm
Abstract. In this talk we will review and discuss various aspects of multi-stage decision optimization problems under uncertainty – from problem formulation to modeling language support as well as the numerical solution of optimization problems. A stylized example is used to provide a complete walk-through using open-source software. In this presentation, the numerical solution is based on techniques from the field of multi-stage stochastic programming. A crucial issue is the proposed simplification of current modeling language approaches to annotate multi-stage optimization programs in order to e.g. allow for creating multi-stage optimization model libraries, which are independent of the underlying solution method. Selected multi-stage models from the area of Finance and Energy will be presented.
About the speaker. Ronald Hochreiter is Docent at the Department of Finance, Accounting and Statistics at the WU Vienna University of Economics and Business. He loves optimization under uncertainty and enjoys to think about how to simplify the modeling process of complex decision problems as well as how to implement optimization modeling tools for specific application areas. Lately, he also likes to conduct classical Business Analytics tasks for data-related problems from areas as diverse as Finance, Public Policy, and Health Care.

Seminar: Medium-term planning for thermal electricity production
2014-07-03 14:00
Title: Medium-term planning for thermal electricity productionSpeaker: Dr. Florentina ParaschivAffiliation: Institute for Operations Research and Computational Finance – University of St. GallenLocation: Room 218 Huxley BuildingTime: 2:00pm
Abstract. In the present paper, we present a mid-term planning model for thermal power generation which is based on multistage stochastic optimization and involves stochastic electricity spot prices, a mixture of fuels with stochastic prices, the effect of CO2 emission prices and various types of further operating costs. Going from data to decisions, the first goal was to estimate simulation models for various commodity prices. We apply Geometric Brownian motions with jumps to model gas, coal, oil and emission allowance spot prices. Electricity spot prices are modeled by a regime switching approach which takes into account seasonal effects and spikes. Given the estimated models, we simulate scenario paths and then use a multiperiod generalization of the Wasserstein distance for constructing the stochastic trees used in the optimization model. Finally, we solve a 1-year planning problem for a fictitious configuration of thermal units, producing against the markets. We use the implemented model to demonstrate the effect of CO2 prices on cumulated emissions and to apply the indifference pricing principle to simple electricity delivery contracts.
About the speaker. Dr. Florentina Paraschiv is an Assistant Professor at the University of St. Gallen and she works inside the Institute for Operations Research and Computational Finance ior/cf-HSG. Her interest fields include: econometrics of electricity, oil, and gas markets, quantification of risk in the electricity business, optimization of power production, renewable energy.

Seminar: High-precision solutions for linear programs over the rational numbers
2014-07-09 15:00
Title: High-precision solutions for linear programs over the rational numbersSpeaker: Ambros GleixnerAffiliation: Zuse Institute BerlinLocation: CPSE seminar room (C615 Roderic Hill)Time: 3:00pm
Abstract.
About the speaker.

Seminar: Bayesian Optimization for Learning Robot Control
2014-10-17 15:00
Title: Bayesian Optimization for Learning Robot ControlSpeaker: Dr. Marc DeisenrothAffiliation: Department of Computing – Imperial College LondonLocation: Room 217 Huxley BuildingTime: 3:00pm
Abstract. Statistical machine learning has been a promising direction in control and robotics for more than a decade since data-driven learning allows us to reduce the amount of engineering knowledge that is otherwise required. In real systems, such as robots, many experiments can be impractical and time consuming. I will discuss Bayesian optimization, an approach to controller learning that is based on efficient global optimization of black-box (utility) functions, in the context of robot learning. I will demonstrate that this kind of learning is (a) practical and (b) very fast, i.e., it requires only a few experiments, to learn good controller parameterizations for a bipedal robot.
About the speaker. Marc is PI of the SML group and an Imperial College Junior Research Fellow (tenure-track) with interests in statistical machine learning, robotics, control, time-series analysis, and signal processing. Marc joined the Department of Computing as a Research Fellow in September 2013. From December 2011 to August 2013 he was a Senior Research Scientist & Group Leader (Learning for Control) at TU Darmstadt (Germany). Marc is still adjunct researcher at TU Darmstadt. From February 2010 to December 2011, he was a full-time Research Associate at the University of Washington (Seattle). Marc completed his PhD at the Karlsruhe Institute for Technology (Germany) in 2009. He conducted his PhD research at the Max Planck Institute for Biological Cybernetics (2006–2007) and at the University of Cambridge (2007–2009). Marc’s research interests center around methodologies from modern Bayesian machine learning and their application autonomous control and robotic systems. Marc’s goal is to increase the level of autonomy in robotic and control systems by modeling and accounting for uncertainty in a principled way. Potential applications include intelligent prostheses, autonomous robots, and healthcare assistants.

Seminar: Visual-Inertial Odometry (VIO) Using Nonlinear Optimization
2014-10-30 14:00
Title: Visual-Inertial Odometry (VIO) Using Nonlinear OptimizationSpeaker: Dr. Stefan LeuteneggerAffiliation: Dyson Robotics Lab – Imperial College LondonLocation: Room 217 Huxley BuildingTime: 2:00pm
Abstract. Visual-inertial fusion for state estimation and mapping has recently drawn increased attention. The sensing modalities offer compelling complementary characteristics, since inertial measurements provide strong short-term temporal correlations, while visual correspondences in images form spatial (relative pose) correlations. Furthermore, inertial MEMS sensors have become increasingly small, cheap, and accurate. Traditionally, the visual-inertial odometry problem has been rather addressed with filtering formulations; in this seminar, however, an approach using nonlinear optimization is presented — inspired by recent work of the computer vision community solving large reconstruction problems using optimization. The full batch VIO problem becomes untractable quite quickly; mobile robotics, however, needs to comply with real-time constraints. To this end, a framework using partial linearization of error terms along with marginalization (variable elimination) is suggested that allows for a bounded optimization window using the notion of keyframes without compromising the inherent sparsity of the problem. We will go through the necessary mathematical machinery and present a quantitative evaluation as well as qualitative results from on-board Unmanned Aerial Systems (UAS).
About the speaker. Stefan Leutenegger has obtained his PhD from ETH Zurich (Autonomous Systems Lab, ASL) in 2014, where he has has worked on solar airplane design from concepts to realization and flight testing, as well as related algorithms for navigation close to the terrain. His activities covered a broad range from structural, electrical and software engineering to the development of highly efficient, robust, and accurate algorithms for multi-sensor state estimation and mapping. As part of his PhD work, Stefan spent three months at the robotics company Willow Garage in Menlo Park, California, in 2012 under the supervision of Dr. Kurt Konolige and Dr. Vincent Rabaud. Besides his involvement in engineering and science activities, Stefan had the ASL-internal lead in the European FP7 Projects “ICARUS” and “SHERPA” since the proposal writing phase. He has furthermore been involved in BSc and MSc student project supervision as well as for teaching a part of ASL’s Master course on Unmanned Aerial Systems. In October 2014, Stefan started as a lecturer of robotics at Imperial College London, working in Andy Davison’s Dyson Robotics Laboratory.

Seminar: Static and Dynamic Assortment Optimization
2014-12-11 14:00
Title: Static and Dynamic Assortment OptimizationSpeaker: Prof. Kalyan TalluriAffiliation: Imperial College London Business SchoolLocation: LT 311 Huxley BuildingTime: 2:00pm
Abstract. Assortment Optimization is the problem of offering an optimal assortment from a ground set. Customers choose one of the offered products or decide not to purchase any. The dynamic version of this problem with finite inventories and time is a model for revenue management. Both problems are difficult when the customer population is heterogeneous (multiple segments). In this talk we present our research on the computational approaches for static and dynamic optimization under the choice as well as a matching model.
About the speaker. Kalyan Talluri is Professor of Operations Management at Imperial College London Business School, London. Previously he was an ICREA Research Professor in the Department of Economics and Business at the Universitat Pompeu Fabra in Barcelona. He got his Masters from Purdue University and a Ph.D in Operations Research from MIT. He has taught at the Kellogg School of Management, Northwestern University, Indian School of Business, Tuck School of Management, Dartmouth, IESE and INSEAD. His research interests are in pricing of consumer goods and services and the operational implementation of pricing tactics. He has published in OR and Management journals and is the co-winner of the INFORMS Lanchester Prize for the year 2005. He is the co-author of the book “Theory and Practice of Revenue Management”.

Seminar: Markov Random Field Optimization in Medical Image Analysis
2015-01-13 14:00
Title: Markov Random Field Optimization in Medical Image AnalysisSpeaker: Dr. Ben GlockerAffiliation: Department of Computing – Imperial College LondonLocation: Room 140 HuxleyTime: 2:00pm
Abstract. Markov Random Fields (MRFs) are widely used for modelling image analysis problems, such as segmentation, denoising, and motion estimation. In this presentation, I will provide a brief overview of different applications of MRFs and some of the commonly used energy models and optimization methods. In particular, recent advances in higher-order MRF optimization seem a promising direction for modelling more complex and sophisticated energies. However, computational performance could be a limiting factor when scaling those models to large image databases. A potential solution could be to employ efficient discrete-continuous optimization methods.
About the speaker. Ben Glocker is a Lecturer in Medical Image Computing at the Department of Computing, Imperial College London. Before joining Imperial in October 2013, he has been working as a post-doctoral researcher in the Machine Learning & Perception Group at Microsoft Research Cambridge. He has been appointed as Researcher Fellow of Darwin College, University of Cambridge, from 2010-2012. Ben received his doctoral degree from the Technical University of Munich, in 2011. Ben is a member of the Biomedical Image Analysis group. His research focus is on advanced methods and tools for biomedical image computing and computer vision. In particular, he is interested in semantic understanding and automatic analysis of images using machine learning techniques.

Seminar: Bayesian Optimization
2015-02-04 14:00
Title: Bayesian Optimization Speaker: Dr. Mike OsborneAffiliation: Department of Engineering Science – University of Oxford Location: Room 145 HuxleyTime: 2:00pm
Abstract.
About the speaker.

Seminar: McCormick Relaxations: Convergence Rate and Extension to Multivariate Outer Functions
2015-02-06 15:00
Title: McCormick Relaxations: Convergence Rate and Extension to Multivariate Outer FunctionsSpeaker: Prof. Alexander MitsosAffiliation: Laboratory for Process Systems Engineering – RWTH Aachen UniversityLocation: CPSE seminar room (C615 Roderic Hill)Time: 3:00pm
Abstract. Optimization is a widely used tool in process systems engineering, but often the optimization problems have multiple suboptimal local minima. Deterministic global optimization algorithms can solve such problems, typically employing convex/concave relaxations of the objective and constraints. Several methods have been proposed for the construction of convergent relaxations, including the McCormick relaxations. These provide the framework for the computation of convex relaxations of composite functions. McCormick’s relaxations are clearly a very important tool, but they have the limitation of only allowing univariate composition. Although most functions can be decomposed in a way that only univariate functions are used as building blocks, this often results in weak relaxations. Moreover, McCormick has not provided results for the convergence rate of these relaxations. We propose a reformulation of McCormick’s composition theorem, which while equivalent to the original, suggests a straight forward generalization to multi-variate outer functions. In addition to extending the framework, the multi-variate McCormick relaxation is a useful tool for the proof of relaxations: by direct application to the product, division and minimum/maximum of two functions, we obtain improved relaxations when comparing with uni-variate McCormick. Furthermore, we generalize the theory for the computation of subgradients to the multi-variate case, envisioning practical methods that utilize the framework. Further, we extend the notion of convergence order from interval extensions to convex relaxations in the pointwise metric and Hausdorff metric. We develop theory for the McCormick relaxations by establishing convergence rules for the addition, multiplication and composition operations. The convergence order of the composite function depends on the convergence order of the relaxations of the factors. No improvement in the order of convergence compared to that of the underlying bound calculation, e.g., via interval extensions, can be guaranteed unless the relaxations of the factors have pointwise convergence of high order, in which case at least quadratic conver- gence order can be guaranteed. Additionally, the McCormick relaxations are compared with the alphaBB relaxations by Floudas and coworkers, which also guarantee quadratic pointwise convergence. Finally, the convergence order of McCormick-Taylor models is addressed. Illustrative and numerical examples are given and hybrid methods are discussed. The implication of the results are discussed for practical bound calculations as well as for convex/concave relaxations of factors commonly found in process systems engineering models.
About the speaker. Alexander Mitsos is a Full Professor (W3) in RWTH Aachen University, and the Director of the Laboratory for Process Systems Engineering (AVT.SVT), comprising 40 research and administrative staff. Mitsos received his Dipl-Ing from University of Karlsruhe in 1999 and his Ph.D. from MIT in 2006, both in Chemical Engineering. Prior appointments include military service, free-lance engineering, involvement in a start-up company, a junior research group leader position in the Aachen Institute of Computational Engineering Science and the Rockwell International Assistant Professorship at MIT. Mitsos has over 60 publications in peer-reviewed journals and has received a number of awards. His research focuses on optimization of energy and chemical systems and development of enabling numerical algorithms.

Seminar: Worst-case complexity of nonlinear optimization: Where do we stand?
2015-02-11 11:00
Title: Worst-case complexity of nonlinear optimization: Where do we stand?Speaker: Prof. Philippe TointAffiliation: Department of Mathematics – Université de NamurLocation: CPSE seminar room (C615 Roderic Hill)Time: 11:00am
Abstract. We review the available results on the evaluation complexity of algorithms using Lipschitz-continuous Hessians for the approximate solution of nonlinear and potentially nonconvex optimization problems. Here, evaluation complexity is a bound on the largest number of problem functions (objective, constraints) and derivatives evaluations that are needed before an approximate first-order critical point of the problem is guaranteed to be found. We start by considering the unconstrained case and examine classical methods (such as Newton’s method) and the more recent ARC2 method, which we show is optimal under reasonable assumptions. We then turn to constrained problems and analyze the case of convex constraints first, showing that a suitable adaptation ARC2CC of the ARC2 approach also possesses remarkable complexity properties. We finally extend the results obtained in simpler settings to the general equality and inequality constrained nonlinear optimization problem by constructing a suitable ARC2GC algorithm whose evaluation complexity also exhibits the same remarkable properties.
About the speaker. Philippe L. Toint (born 1952) received its degree in Mathematics in the University of Namur (Belgium) in 1974 and his Ph.D. in 1978 under the guidance of Prof M.J.D. Powell. He was appointed as lecturer at the University of Namur in 1979 were he became associate professor in 1987 and full-professor in 1993. Since 1979, he has been the co-director of the Numerical Analysis Unit and director of the Transportation Research Group in this department. He was in charge of the University Computer Services from 1998 to 2000 and director of the Department of Mathematics from 2006 to 2009. He currently serves as Vice-rector for Research and IT for the university. His research interests include numerical optimization, numerical analysis and transportation research. He has published four books and more than 280 papers and technical reports. Elected as SIAM Fellow (2009), he was also awarded the Beale-Orchard-Hayes Prize (1994, with Conn and Gould)) and the Lagrange Prize in Continuous Optimization (2006, with Fletcher and Leyffer). He is the past Chairman (2010-2013) of the Mathematical Programming Society, the international scientific body gathering most researchers in mathematical optimization world-wide. Married and father of two girls, he is a keen music and poetry lover as well as an enthusiast scuba-diver.

Seminar: Formal Proofs for Nonlinear Optimization
2015-03-03 14:00
Title: Formal Proofs for Nonlinear OptimizationSpeaker: Dr. Victor MagronAffiliation: Department of Electrical and Electronic Engineering – Imperial College LondonLocation: Room 217 Huxley BuildingTime: 2:00pm
Abstract. We present a formally verified global optimization framework. Given a semialgebraic or transcendental function f and a compact semialgebraic domain K, we use the nonlinear maxplus template approximation algorithm to provide a certified lower bound of f over K. This algorithm allows to bound in a modular way some of the constituents of f by suprema of quadratic forms with a well chosen curvature. Thus, we reduce the initial goal to a hierarchy of semialgebraic optimization problems, solved by semidefinite relaxations. Our implementation tool interleaves semialgebraic approximations with sums of squares witnesses to form certificates. It is interfaced with Coq and thus benefits from the trusted arithmetic available inside the proof assistant. This feature is used to produce, from the certificates, both valid underestimators and lower bounds for each approximated constituent. The application range for such a tool is widespread; for instance Hales’ proof of Kepler’s conjecture yields thousands of multivariate transcendental inequalities. We illustrate the performance of our formal framework on some of these inequalities as well as on examples from the global optimization literature.http://cas.ee.ic.ac.uk/people/vmagron/slides/quads.pdf
About the speaker. Victor graduated from Ecole Centrale Paris Engineering School in 2010, while receiving his MSc from the department of Systems Innovation, Tokyo University (double diploma). In 2013, he received his PhD in Computer Science at INRIA Saclay, Ecole Polytechnique. In 2014, he was a Postdoc fellow in the MAC team at LAAS in Toulouse, France. He is currently a Research Assistant at Imperial College for the Circuits and Systems group, in the department of Electrical and Electronic Engineering.

Seminar: Supply Chain Optimization - from strategic to operational decision levels
2015-03-13 15:00
Title: Supply Chain Optimization – from strategic to operational decision levelsSpeaker: Prof. Ana Barbosa-PovoaAffiliation: University of LisbonLocation: CPSE seminar room (C615 Roderic Hill)Time: 3:00pm
Abstract. Supply Chains are complex systems that involve challenging problems. Such problems require suitable answers so as to guarantee efficiency and responsiveness improvements of the involved systems. When answering to such problems optimization is a possible path to follow aiming at building tools that can help the decision makers on the problems solutions that span from strategic to operational levels. The scientific community has been exploring this pathway but much more is required, especially due to the outer shell of new emerging problems. The present talk characterizes supply chain decisions and presents some of the work that has been done on the optimization of supply chains detailing specially the work developed by the Operations and Logistics Group of the Centre for Management Studies at Instituto Superior Técnico (IST) in Lisbon. We conclude with a discussion of the tendencies and future challenges in the area.
About the speaker. Ana Barbosa-Póvoa obtained her PhD in Engineering from Imperial College of Science Technology and Medicine. She is currently a Full Professor of Operations and Logistics at the Department of Management and Engineering of Instituto Superior Técnico (IST), University of Lisbon, Portugal where she is the director of the BSc and Master Programs in Engineering and Management. She is a member of the scientific council of IST and of the University Senate. She is also the Vice-president of the Portuguese Association for Operational Research. She has been acting as reviewer to several national and international research scientific boards on research projects. Her research interests are on the supply chain management, where both forward and reserve structures are included and on the design, planning and scheduling of flexible systems. Ana has published widely in these areas and supervised several Master and PhD students. Ana in 2008 has received the scientific award of Technical University of Lisbon in the scientific area of Industrial Management.

Seminar: Bifurcation Analysis Using Complete Search Methods
2015-03-17 14:00
Title: Bifurcation Analysis Using Complete Search Methods Speaker: Dr. Mario Eduardo VillanuevaAffiliation: Centre for Process Systems Engineering at Imperial CollegeLocation: Room 217 Huxley BuildingTime: 2:00pm
Abstract. When studying a non-linear dynamic system it is important to locate and characterise its equilibrium manifold and its bifurcation regions within a pre-specified computational domain. Except for very few simple cases, an algebraic characterisation of such manifold is impossible. In this seminar a methodology for locating the equilibrium manifold of non-linear dynamic systems defined by parametric ODEs is presented. This methodology is based on a set-inversion approach which uses state-of-the-art bounding techniques within a complete search algorithm. The efficacy of this approach is illustrated with a challenging non-linear model of an anaerobic digestion process.
About the speaker. Mario Eduardo Villanueva (MEV) graduated with a BEng in Biochemical Engineering from the Instituto Tecnologico de Veracruz, Mexico and an MSc in Advanced Chemical Engineering with Process Systems Engineering from Imperial College London. He is currently a PhD student in the Department of Chemical engineering, under the supervision of Dr. B. Chachuat. His PhD project is concerned with the development of methods and tools for complete search in uncertain dynamic systems.

Seminar: The Complexity of Primal-Dual Fixed Point Methods for Ridge Regression
2015-03-25 14:00
Title: The Complexity of Primal-Dual Fixed Point Methods for Ridge RegressionSpeaker: Prof. Ademir RibeiroAffiliation: Department of Mathematics – Federal University of ParanaLocation: Room 218 Huxley BuildingTime: 2:00pm
Abstract. We study the ridge regression (L2 regularized least squares) problem and its dual, which is also a ridge regression problem. We observe that the optimality conditions can be formulated in several different but equivalent ways, in the form of a linear system involving a structured matrix depending on a single “stepsize” parameter which we introduce for regularization purposes. This leads to the idea of studying and comparing, in theory and practice, the performance of the fixed point method applied to these reformulations. We compute the optimal stepsize parameters and uncover interesting connections between the complexity bounds of the variants of the fixed point scheme we consider. These connections follow from a close link between the spectral properties of the associated matrices. For instance, some reformulations involve purely imaginary eigenvalues; some involve real eigenvalues and others have all eigenvalues on the complex circle. We show that the deterministic Quartz method—which is a special case of the randomized dual coordinate ascent method with arbitrary sampling recently developed by Qu, Richtarik and Zhang—can be cast in our framework, and achieves the best rate in theory and in numerical experiments among the fixed point methods we study. This is joint work with Peter Richtarik (Edinburgh).
About the speaker. I am an Associate Professor at Department of Mathematics, Federal University of Parana, Brazil, since 1992. I got my undergraduate degree in Mathematics at Federal University of Parana in 1989. In 1993 I finished my MSc in Mathematics, at IMPA – National Institute for Pure and Applied Mathematics. I got my PhD in Optimization at Federal University of Parana in 2005. My current research interests are applied mathematics, continuous optimization, global and local convergence of algorithms as filter and trust region methods for nonlinear programming and convex optimization, complexity of direct search methods, among others. I have been published papers in journals like Applied Mathematics and Computation, Applied Mathematical Modelling, Optimization, Computational Optimization and Applications, Mathematical Programming and SIAM Journal on Optimization. I have been given talks in some meetings like Optimization Conference (Porto 2007 and Guimarães 2014), Brazilian Workshop on Continuous Optimization (Rio de Janeiro 2009 and Florianópolis 2014) and International Symposium on Mathematical Programming (Rio de Janeiro 2006 and Berlin 2012). I have supervised 2 PhD and 6 MSc students. In joint work with Elizabeth Wegner Karas, I also have published a book (in Portuguese), called Continuous Optimization: Theoretical and computational aspects. Cengage Learning, Sao Paulo, Brazil, 2013.

Seminar: Are Targets for Renewable Portfolio Standards Too Low? - The Impact of Market Structure on Energy Policy? (joint work with Makoto Tanaka and Yihsu Chen)
2015-04-13 14:00
Title: Are Targets for Renewable Portfolio Standards Too Low? – The Impact of Market Structure on Energy Policy? (joint work with Makoto Tanaka and Yihsu Chen)Speaker: Dr Afzal SiddiquiAffiliation: Department of Statistical Science – University College LondonLocation: Room 217 Huxley BuildingTime: 2:00pm
Abstract. In order to limit climate change from greenhouse gas emissions, governments have introduced renewable portfolio standards (RPS) to incentivize renewable energy production. While the response of industry to exogenous RPS targets has been addressed in the literature, setting RPS targets from a policymaker’s perspective has remained an open question. Using a bi-level model, we prove that the optimal RPS target for a perfectly competitive electricity industry is higher than that for a benchmark centrally planned one. Allowing for market power by the non-renewable energy sector within a deregulated industry lowers the RPS target vis-à-vis perfect competition. Moreover, to our surprise, social welfare under perfect competition with RPS is lower than that when the non-renewable energy sector exercises market power. In effect, by subsidizing renewable energy and taxing the non-renewable sector, RPS represents an economic distortion that over-compensates damage from emissions. Thus, perfect competition with RPS results in “too much” renewable energy output, whereas the market power of the non-renewable energy sector mitigates this distortion, albeit at the cost of lower consumer surplus and higher emissions. Hence, ignoring the interaction between RPS requirements and the market structure could lead to sub-optimal RPS targets and substantial welfare losses.
About the speaker. Afzal Siddiqui is a Senior Lecturer in the Department of Statistical Science. Previously, he was a Lecturer in Statistics at UCL (2005-2010) and a College Lecturer in the Department of Banking and Finance at University College Dublin. After having completed his Ph.D. in Industrial Engineering and Operations Research from the University of California at Berkeley in 2002, Afzal served as a Visiting Assistant Professor in the Department of Industrial Engineering and Operations Research at UC Berkeley (2002) and a Visiting Post-doctoral Researcher at the Ernest Orlando Lawrence Berkeley National Laboratory (2002-2003). In addition, he is a Professor (20% time) at the Department of Computer and Systems Sciences of Stockholm University and a Visiting Professor at the Systems Analysis Laboratory of Aalto University.

Seminar: A cycle-based formulation and valid inequalities for DC power transmission problems with switching
2015-05-05 15:00
Title: A cycle-based formulation and valid inequalities for DC power transmission problems with switchingSpeaker: Prof. Jeff LinderothAffiliation: Departments of Industrial and Systems Engineering and Computer Sciences (by courtesy) – University of Wisconsin-MadisonLocation: LT 145 Huxley BuildingTime: 3:00pm
Abstract. It is well-known that optimizing network topology by switching on and off transmission lines improves the efficiency of power delivery in electrical networks. Many authors have studied the problem of determining an optimal set of transmission lines to switch off to minimize the cost of meeting a given power demand under the direct current (DC) model of power flow. This problem is known in the literature as the Direct-Current Optimal Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on heuristic algorithms for generating quality solutions or on the application of DC-OTS to crucial operational and strategic problems. The mathematical theory of the DC-OTS problem is less well-developed. In this work, we formally establish that DC-OTS is NP-Hard, even if the power network is a series-parallel graph with at most one load/demand pair. Inspired by Kirchoff’s Voltage Law, we give a cycle-based formulation for DC-OTS, and we use the new formulation to build a cycle-induced relaxation. We characterize the convex hull of the cycle-induced relaxation, and the characterization provides strong valid inequalities that can be used in a cutting-plane approach to solve the DC-OTS. We give details of a practical implementation, and we show promising computational results on standard benchmark instances. Co-authors:This is joint work with: Burak Kocuk, Santanu Dey, Andy Sun (Georgia Tech), Hyemin Jeon, and Jim Luedtke (Wisconsin)
About the speaker. Jeff Linderoth is a Professor in the departments of Industrial and Systems Engineering and Computer Sciences (by courtesy) at the University of Wisconsin-Madison, joining both departments in 2007. Dr. Linderoth received his Ph.D. degree from the Georgia Institute of Technology in 1998. He was awarded an an Early Career Development Award from the Department of Energy, and he has won the SIAM/Activity Group on Optimization Prize and the INFORMS Computing Society ICS Prize. Dr. Linderoth currently serves on the editorial boards of 4 journals, including Operations Research and Mathematical Programming Computation.
