Seminar: Interdiction Games on Markovian PERT Networks
2013-07-03 15:00 UTC
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.

Seminar: A bilevel programming problem occurring in smart grids
2015-05-07 11:00
Title: A bilevel programming problem occurring in smart gridsSpeaker: Prof. Leo LibertiAffiliation: Ecole Polytechnique ParisLocation: CPSE seminar room (C615 Roderic Hill)Time: 11:00am
Abstract. A key property to define a power grid “smart” is its real-time, fine-grained monitoring capabilities. For this reason, a variety of monitoring equipment must be installed on the grid. We look at the problem of fully monitoring a power grid by means of Phasor Measurement Units (PMUs), which is a graph covering problem with some equipment-specific constraints. We show that, surprisingly, a bilevel formulation turns out to provide the most efficient algorithm.
About the speaker. Leo Liberti obtained his B.Sc. in Mathematics and his Ph.D. in Process Systems Engineering from Imperial College. He became a professor at Ecole Polytechnique (France), then a Research Staff Member at IBM Research (USA). He was recently appointed Research Director at CNRS and part-time professor back at Ecole Polytechnique. His research interests are Mixed-Integer Nonlinear Programming and Distance Geometry.

Seminar: Computational Progress in Linear and Mixed Integer Programming
2015-05-13 11:00
Title: Computational Progress in Linear and Mixed Integer ProgrammingSpeaker: Dr. Robert BixbyAffiliation: GurobiLocation: CPSE seminar room (C615 Roderic Hill)Time: 11:00am
Abstract. We will look at the progress in linear and mixed-integer programming software over the last 25 years. As a result of this progress, modern linear programming codes are now capable of robustly and efficiently solving instances with multiple millions of variables and constraints. With these linear programming advances as a foundation, mixed-integer programming then provides the modeling framework and solution technology that enables the overwhelming majority of present-day business planning and scheduling applications, and is the key technology behind prescriptive analytics. The performance improvements in mixed-integer programming code overs the last 25 years have been nothing short of remarkable, well beyond those of linear programming and have transformed this technology into an out-of-the box tool with applications to an almost unlimited range of real-world problems.
About the speaker.

Seminar: Estimating variance matrices
2015-05-19 14:00
Title: Estimating variance matricesSpeaker: Prof. Karim Abadir Affiliation: Imperial College Business SchoolLocation: Room 218 Huxley BuildingTime: 2:00pm
Abstract. ﻿ This talk introduces a new method for estimating variance matrices. Starting from the orthogonal decomposition of the sample variance matrix, we exploit the fact that orthogonal matrices are never ill-conditioned and therefore focus on improving the estimation of the eigenvalues. We estimate the eigenvectors from just a fraction of the data, then use them to transform the data into approximately orthogonal series that deliver a well-conditioned estimator (by construction), even when there are fewer observations than dimensions. We also show that our estimator has lower error norms than the traditional one. Our estimator is design-free: we make no assumptions on the distribution of the random sample or on any parametric structure the variance matrix may have. Simulations confirm our theoretical results and they also show that our simple estimator does very well in comparison with other existing methods, especially when the data are generated from fat-tailed densities.
About the speaker. ﻿ Karim Abadir is the Chair of Financial Econometrics at Imperial College, London. He obtained his DPhil from Oxford University. His MA (Economics) and BA (Major in Economics, Minor in Business) are from the American University in Cairo. He started his academic career as a lecturer in Economics at Lincoln College, Oxford. He then joined the University of Exeter as a Senior Lecturer in Statistics and Econometrics, rising to the position of Reader in Econometrics. From 1996-2005, he held a Chair in Econometrics and Statistics at the University of York, joint between the Departments of Mathematics and Economics.He is credited with having solved in his DPhil a major long-standing problem in Mathematical Statistics and Time Series that was open since the 1950’s. More recently, he has predicted the timing of the 2008 recession a year in advance, and the different timings of the recoveries in various Western countries.He is a founding member of the liberal party Al Masreyeen Al Ahrrar (translates as Free/Liberal Egyptians), established in 2011.

Seminar: A two-phase proximal augmented Lagrangian method for large scale convex composite quadratic programming
2015-09-02 11:00
Title: A two-phase proximal augmented Lagrangian method for large scale convex composite quadratic programmingSpeaker: Prof. Kim Chuan TohAffiliation: Department of Mathematics – National University of SingaporeLocation: CPSE seminar room (C615 Roderic Hill)Time: 11:00am
Abstract. We consider an important class of high dimensional convex composite quadratic optimization problems with large numbers of linear equality and inequality constraints. Our work is motivated by the recent interests in convex quadratic conic programming problems, as well as from convex quadratic programming problems with dual block angular structures such as those arising from two stage stochastic programming problems. In this talk, we first introduce a symmetric Gauss-Seidel (sGS) decomposition theorem for solving an unconstrained convex composite programming problem whose objective is the sum of a multi-block quadratic function and a non-smooth function involving only the first block. Then, based on the sGS decomposition theorem, we propose a two phase proximal augmented Lagrangian method to efficiently solve the targeted problem to high accuracy. Specifically, in Phase I, we design an inexact sGS-based semi-proximal ADMM to generate a reasonably good initial point to warm-start the algorithm in Phase II, which is a semi-smooth NewtonCG based proximal augmented Lagrangian method capable of computing a high accuracy solution efficiently.
About the speaker. Kim-Chuan Toh is a Professor at the Department of Mathematics, National University of Singapore (NUS). He obtained his Bachelor degree from NUS in 1990 and the PhD degree from Cornell University in 1996 under the guidance of Professor Nick Trefethen. He is currently an Area Editor for Mathematical Programming Computation, and an Associate Editor for the SIAM Journal on Optimization. His research focuses on designing efficient algorithms and software for convex programming, particularly large scale matrix optimization problems such as semidefinite programming (SDP) and convex quadratic SDP.

Seminar: Generating structured music with local search and machine learning
2015-10-14 15:30
Title: Generating structured music with local search and machine learningSpeaker: Dr. Dorien HerremansAffiliation: School of Electronic Engineering and Computer Science – Queen Mary UniversityLocation: LT 144 Huxley BuildingTime: 3:30pm
Abstract. Many state of the art music generation/improvisation systems generate music that sounds good on a note-to-note level. However, these compositions often lack long term structure or coherence. By looking at generating music as an optimization problem, this research overcomes this problem and generates music that has a larger structure. A powerful variable neighbourhood search algorithm (VNS) was developed, which is able to generate a range of musical styles based on it’s objective function, whilst constraining the music to a structural template. In the first stage of the project, an objective function based on rules from music theory was used to generate counterpoint. In this research, a machine learning approach is combined with the VNS in order to generate structured music for the bagana, an Ethiopian lyre. Different ways are explored in which a Markov model can be used to construct quality metrics that represent how well a fragment fits the chosen style (e.g. music for bagana). Current research that aims to extend the objective function with models such as recursive neural networks is also briefly discussed. The approach followed in this research allows us to combine the power of machine learning methods with optimization algorithms.
About the speaker. Dorien Herremans is currently a Marie Skodowska-Curie Postdoctoral Fellow at C4DM, Queen Mary University of London. She got her PhD in Operations Research on the topic of Computer Generation and Classification of Music through Operations Research Methods (Compose: Compute – Generating and Classifying Music through Operations Research Methods). She graduated as a commercial engineer in management information systems at the University of Antwerp in 2005. After that, she worked as a Drupal consultant and was an IT lecturer at the Les Roches University in Bluche, Switzerland. She also worked as a mandaatassistent at the University of Antwerp, in the domain of operations management, supply chain management and operations research (OR). Her current research focuses on applications of OR in the field of music.

Seminar: Families of Convex and Non-Convex Composite Optimization Problems for Signal Processing and Computer Vision
2015-10-16 15:00
Title: Families of Convex and Non-Convex Composite Optimization Problems for Signal Processing and Computer VisionSpeaker: Dr. Stefanos ZafeiriouAffiliation: Department of Computing – Imperial College LondonLocation: Room 217 – 218 Huxley BuildingTime: 3:00pm
Abstract.
About the speaker. Stefanos Zafeiriou is a Senior Lecturer (equivalent to Associate Professor) in Pattern Recognition/Statistical Machine Learning for Computer Vision in the Department of Computing, Imperial College London. He has been awarded one of the prestigious Junior Research Fellowships (JRF) from Imperial College London in 2011 to start his own independent research group. He is/has participated in more than 10 EU, British and Greek research projects. Dr. Zafeiriou currently serves as an Associate Editor in IEEE Transactions on Cybernetics and Image and Vision Computing journal. He has been guest editor in more than four special issues and co-organized more than five workshops/ special sessions in top venues such as CVPR/FG/ICCV/ECCV. He has co-authored more than 40 journal papers mainly on novel statistical machine learning methodologies applied to computer vision problems such as 2D/3D face and facial expression recognition, deformable object tracking, human behaviour analysis etc published in the most prestigious journals in his field of research (such as IEEE T-PAMI, IJCV, IEEE T-IP, IEEE T-NNLS, IEEE T-VCG, IEEE T-IFS etc). His students are frequent recipients of very prestigious and highly competitive fellowships such as Google Fellowship, Intel Fellowship and the Qualcomm fellowship. He has more than 2000 citations to his work, h-index 24.

Seminar: Rescaled coordinate descent methods for Linear Programming
2015-12-01 16:00
Title: Rescaled coordinate descent methods for Linear ProgrammingSpeaker: Dr. Giacomo ZambelliAffiliation: Department of Management – London School of Economics and Political ScienceLocation: SALC 10 Sherfield Building Time: 4:00pm
Abstract. Simple coordinate descent methods such as von Neumann’s algorithm or Perceptron, both developed in the 50s, can be used to solve linear programming feasibility problems. Their convergence rate depends on the condition measure of the problem at hand, and is typically not polynomial. Recent work of Chubanov (2012, 2014), related to prior work of Betke (2004), has gathered renewed interest in the application of these methods in order to obtain polynomial time algorithms for linear programming. We present two algorithms that fit into this line of research. Both our algorithms alternate between coordinate descent steps and rescaling steps, so that either the descent step leads to a substantial improvement in terms of the convergence, or we can infer that the problem is ill conditioned and rescale in order to improve the condition measure. In particular, both algorithms are based on the analysis of a geometrical invariant of the LP problem, used as a proxy for the condition measure, that appears to be novel in the literature. This is joint work with Daniel Dadush (CWI) and László Végh (LSE)
About the speaker. Dr Zambelli is an Associate Professor (Reader) in the Department of Mathematics at the London School of Economics and Political Science, which he joined in September 2010. Previously he was Assistant Professor at the University of Padova. He completed his PhD in Algorithms, Combinatorics and Optimization at the Tepper School of Business, Carnegie Mellon University. He is a co-recipient of the 2015 INFORMS Lanchester Prize.
