2009 Seminars

Dr. Allen Holder, Ph.D.

Title: Optimization Problems in Medicine and Biology

Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, IN

Friday, December 4, 2009

2:30 p.m. - 3:30 p.m.

Mohler Lab Room 451

ABSTRACT

The field of mathematical programming is increasingly useful in medicine and biology, and we will discuss some emerging problems. The first will be a problem in medical physics that asks to calculate the beams of radiation that will be used in a radiotherapy treatment. This is one of the three fundamental problems in this research field, and the presentation will develop a new technique based on the P-Median problem that couples it to the other problems. Two problems in computational biology will be discussed. The first is a problem in haplotype inference for which we will identify a subclass of polynomial time problems within an APX-hard problem class. The second is a problem in functional protein alignment that is currently being developed.

BIOGRAPHY

Dr. Holder graduated with a degree in applied mathematics in 1999 from the University of Colorado at Denver. He studies mathematical programming, which permeates and draws from mathematics and computer science. Dr. Holder’s research interests are in applications in Medicine, Medical Physics, Biology, and Economics. He is an Associate Professor of Mathematics at the Rose-Hulman Institute of Technology in Terre Haute, Indiana. He also is the editor of the Mathematical Programming Glossary.


Dr. Reha Tütüncü

Title: Optimization Models in Portfolio Management

Vice President of Goldman Sachs Asset Management

Friday, November 20, 2009

2:30 p.m. - 3:30 p.m.

Mohler Lab Room 451

ABSTRACT

Quantitative investment managers employ a scientific investment process that identifies sources of risk and return. Using this information, portfolios that provide the best trade-off between risks, returns, and trading costs are generated through an optimization process. We discuss some of the recent threads of academic and practitioner research in quantitative portfolio construction including the simultaneous optimization of multiple portfolios and the study of the impact of constraints on optimal portfolios.

BIOGRAPHY

Reha Tütüncü is a Vice President at Goldman Sachs Asset Management where he manages a team responsible for the optimization platform used for quantitative portfolio construction. Prior to joining GSAM, he was an Associate Professor at Carnegie Mellon University. Reha received his Ph.D. in Operations Research from Cornell University. He is the co-author of the book "Optimization Methods in Finance" and the author of many articles on the subjects of optimization and quantitative finance in academic and practitioner journals.


Dr. Warren B. Powell

Title: Approximate Dynamic Programming for High-Dimensional Applications

Department of Operations Research and Financial Engineering, Princeton University

Friday, November 13, 2009

2:30 p.m. - 3:30 p.m.

Mohler Lab Room 451

ABSTRACT

Stochastic resource allocation problems produce dynamic programs with state, information and action variables with thousands or even millions of dimensions, a characteristic we refer to as the "three curses of dimensionality." Classical techniques in approximate dynamic programming solve only part of the problem. We show how the use of the post-decision state variable allows us to break a problem into three distinct components: simulation, deterministic optimization and statistical learning. This strategy decomposes problems over time, allowing us to use commercial packages to solve even large-scale integer programming problems, producing solutions that are optimal at a point in time (given a value function approximation), with approximate (but high quality) solutions over time. The talk will also describe how we have overcome the challenge of estimating value function approximations for complex resource allocation problems, and the critical, but often overlooked, choice of stepsize rule. The methods are illustrated using applications in transportation, spare parts management and energy policy modeling.

BIOGRAPHY

A faculty member at Princeton University since 1981, Professor Powell specializes in stochastic optimization problems arising in a variety of resource allocation problems, with applications encompassing energy resource modeling, transportation, military operations, health and finance. He is the director of CASTLE Laboratory, which has developed planning systems for a wide range of operational problems. He has authored or coauthored over 140 refereed publications, and he is the author of Approximate Dynamic Programming: Solving the curses of dimensionality, published by John Wiley and Sons. His research spans stochastic optimization and the closely related area of optimal learning, which addresses the problem of efficiently collecting information. A recipient of the Informs Fellows Award, Professor Powell has served in a variety of editorial and administrative positions for Informs, including Informs Board of Directors, Area Editor for Operations Research, President of the Transportation Science Section, and numerous prize and administrative committees.


Dr. Stefan Wild

Title: Estimating Computational Noise in Numerical Simulations

Argonne National Laboratory

Friday, October 16, 2009

2:30 p.m. - 3:30 p.m.

Mohler Lab Room 451

ABSTRACT

Computational noise in deterministic simulations is as ill-defined a concept as can be found in scientific computing. Roundoff errors, discretizations, numerical solutions to systems of equations, and adaptive techniques destroy the smoothness of the processes underlying the simulation. Computational noise complicates optimization, sensitivity analysis, and other applications, which depend on the simulation output. In this talk we present examples of computational noise in scientific computing and an algorithm for quantifying this noise.

Following the work of Hamming, we construct a theoretical framework for characterizing stochastic noise using only the computed function values. We present an algorithm based on this framework and show that it usually estimates the computational noise using 6 additional function evaluations. Our numerical tests suggest the algorithm is also effective for deterministic functions, and that it can be used to construct confidence intervals for functions of complex numerical simulations.

Joint work with Jorge More (ANL) and Julio Góez (Lehigh).

BIOGRAPHY

Stefan Wild received his Ph.D. from the School of Operations Research & Information Engineering at Cornell University in 2008. His work at Cornell was supported by a Department of Energy Computational Science Graduate Fellowship. Since then he has been Director's Postdoctoral Fellow at Argonne National Laboratory in the Mathematics & Computer Science Division and the Laboratory for Advanced Numerical Simulations. His research interests are in simulation-based and derivative-free optimization.


Professor Antoine Deza

Title: Computational Approaches to the Hirsch Conjecture in Low Dimension

McMaster University, Hamilton, Ontario, Canada

Tuesday, May 19, 2009

ABSTRACT

Let D(d,n) be the maximal diameter of the edge-graph of a polytope defined by n inequalities in dimension d. The conjecture of Hirsch, formulated in 1957, states that D(d,n) is not greater than n-d. The conjecture relates to the worst case performances of the simplex method of linear programming. No polynomial bound is known for the diameter of a polytope, the best one being quasi-polynominal (Kalai and Kleitman, 1992). In this talk, we will present recent computational approaches to this conjecture, and preliminary results including new entries for D(d,n) in dimensions 4, 5 and 6.

Based on joint-work with David Bremner, University of New Brunswick, William Hua, McMaster University, and Lars Schewe, TU Darmstadt.

BIOGRAPHY

Since 2004, Antoine Deza has been an Associate Professor in the Department of Computing and Software at McMaster University and was awarded a Canada Research Chair in Combintorial Optimization. He has previously helf a faculty position at the Tokyo Institute of Technology, Japan and post-doctoral positions at the Davidson Faculty of Industrial Engineering and Management, Technion, Israel and at the Ecole Polytechnique Federale de Lausanne, Switzerland.


Dr. John Birge

Title: Estimation Effects in Large-Scale Optimization

Professor of Operations Management and Neubauer Family Faculty Fellow Graduate School of Business - University of Chicago

Adjunct Professor, Industrial Engineering and Management Sciences - Northwestern University

Friday, April 10, 2009

ABSTRACT

Increases in computational efficiency lead to the ability to solve ever larger optimization models, but these larger models then require estimation of ever more parameters. In many cases, such as portfolio optimization, the number of these estimates may grow at a greater than linear rate in the number of variables. This talk will describe a model of the effects of estimation errors in optimization models using portfolio optimization and tracking as an example. We will discuss various alternatives for addressing this issue, such as increased sampling, Bayesian views, robust optimization, re-sampling or batching, and model reduction.

BIOGRAPHY

Dr. Birge received his M.S. and Ph.D. degrees from Stanford University in Operations Research. His B.A. is from Princeton University in Mathematics. He is currently the Jerry W. and Carol Lee Levin Professor of Operations Management at the University of Chicago Graduate School of Business. Previously, he was Dean of the McCormick School of Engineering and Applied Science and Professor of Industrial Engineering and Management Sciences at Northwestern University since 1999.

Professor Birge has worked for and has been a consultant to a number of organizations including Morgan Stanley, Deutsche Bank, General Motors, Chrysler Corporation, the Michigan State Senate and the Comision de Regulacion de Energia y Gas in Colombia. He has served as Vice-Chair of the University of Michigan Senate Assembly, as well as Vice President-Subdivisions and President of INFORMS. He has received several grants and is the author of two books, and several publications.


Katya Scheinberg, Ph.D.

Title: Recent Advances in Model Based Derivative Free Optimization

Columbia University Visiting Research Scientist

Friday, March 27, 2009

ABSTRACT

Derivative free optimization addresses general nonlinear optimization problems in the cases when obtaining derivative information for the objective and/or the constraint functions is impractical due to computational cost or numerical inaccuracies. Traditional approaches to derivative free optimization has been based on sampling of the objective function, without any attempt to build models of the function or its derivatives. In the late 90's, model based trust region derivative free methods started to gain popularity. These methods build linear or quadratic interpolation models of the objective function and hence can exploit some first and second order information. We will discuss the lateset developments in the theory and practice of model based DFO methods.

BIOGRAPHY

Katya Scheinberg received her Ph.D. from the Department of Industrial Engineering and Operations Research at Columbia University in 1997. Since then, she has worked as a Research Staff Member in the Mathematical Sciences Department of IBM Research in Yorktown Heights, NY. She is currently visiting Columbia as a research scientist. Her research interests lie in the field of continuous optimization and cover various areas from derivative free optimization to convex optimization, interior point methods and first order methods for convex optimization to applications in machines learning and statistics. She is the author of three open source optimization packages as well as numerous papers covering these subjects.


Robert L. Smith, Ph.D.

Title: Research Funding Opportunities at NSF and Complex Systems Optimization

Program Director for Operations Research - National Science Foundation, Arlington, VA

Friday, March 20, 2009

ABSTRACT

Complex systems consiting of a large number of interacting components are in practice increasingly modeled through computer simulations rather than via traditional equations based approaches. The resulting model typically allows for little or no structural assumptions on the form of the objective function or constraints, thus posing a challenging optimization problem. We will illustrate the approach by discussing an application to intelligent transportation systems.

BIOGRAPHY

Robert L. Smith is the director of Operations Research Program at NSF. Dr. Smith received his Ph.D. in Engineering Science from the University of California at Berkley where he held a NSF Fellowship. He holds a bachelor's degree from Physics from Harvey Mudd College and an MBA from Berkley. He is currently on leave from the University of Michigan in Ann Arbor where he is the Altarum/ERIM Russell D. O'Neal Professor of Engineering.

Dr. Smith is the recipient of the first Altarum/ERIM Russell D. O'Neal Professorshup of Engineering at the University of Michigan. He has also been honored with the Distinguished Faculty Achievement Award from the University of Michigan, the College of Eningeering Research Excellence Award, the Industrial and Operations Engineering Award for Outstanding Accomplishment, an Outstanding Teacher Award from the Michigan Student Assembly, and a NSF Fellowship. He is a fellow of the Institute of Operations Research and the Management Science.


Agostino Capponi, Ph.D. Candidate

Title: Credit Risk Modeling and Valuation

California Institute of Technology

Friday, February 27, 2009

ABSTRACT

Credit Risk is one of the most pervasive threats in today's financial markets. It affects all financial transactions where the credit quality of the counterparty may deteriorate over time, giving rise to potential defaults. Credit risk modeling and valuation is a complex task requiring methods from engineering, tools from mathematics and tractable alogrithms from computer science.

In this talk, we will review standard approaches to credit risk modeling including structural and intensity-based frameworks. We will then introduce credit risk model with incomplete information on the dynamics of the firm's asset value process.

BIOGRAPHY

Agostino Capponi is currently a Ph.D. candidate at the California Institute of Technology. His research addresses the quantitative modeling, valuation and estimation of financial risk, in particular credit risk. He is also interested in the development of engineering methodolgies for calibrating fiancial risk models against real market data. Agostino holds a world patent dealing with state estimation in multi-sensor multi-target tracking systems and has published over ten papers in top level technical journals for financial engineering and statistical signal processing.


Imre Pólik, Ph.D., Visiting Assistant Professor

Title: Applications of Nonstandard Duality Concepts of Conic and Quadratic Optimization

Department of Industrial and Systems Engineering, Lehigh University

Friday, February 20, 2009

ABSTRACT

In this talk, we will present some unusual duality concepts in conic and quadratic optimization and discuss their practical applications. First, we will discuss duality properties of nonconvex quadratic systems, and topics related to the S-lemma. Then we will focus on deriving a strong dual for cone optimization without the usual regularity (Slater) condition. Finally we present duality for cone optimization in absence of exact computations. In each of these three topics, we take away one element of the classical Lagrane-Slater duality theory and see how much of the theory can be salvaged.

BIOGRAPHY

Imre Pólik is a visiting assistant professor of the ISE Department at Lehigh. After finishing his Ph.D. studies at McMaster University under the supervision of Tamás Terlaky, he was a postdoctoral research fellow at the School of Computational Engineering and Science, McMaster University, Canada. His primary research interest is in high performance computing and concic optimization.


Pietro Belotti, Ph.D., Visiting Assistant Professor

Title: Disjunctions in Mixed-Integer Nonlinear Programming: Branching Techniques and Inequalities

Department of Industrial and Systems Engineering, Lehigh University

Tuesday, February 17, 2009

ABSTRACT

Exact Solvers for Mixed-Integer Nonlinear Programming (MINLP) problems have to cope with two types of nonconvexity: the integrality of variables and continuous nonconvex functions. Both types of nonconvexity can be dealt with by means of disjunctions that divide the feasible set in two or more subsets. We discuss a straightforward exentsion of disjunctive cuts to the MINLP case and present some computational results to assess the use disjunctions in both the branching and cutting plane steps.

BIOGRAPHY

Pietro Belotti is a visiting assistant professor of the ISE Department at Lehigh. He received his Ph.D. in Computer Engineering from the Technical University of Milan in 2003, with a dissertation on the problem of designing survivable telecommunication networks. His main research interests are Mixed-Integer Nonlinear Programming, Telecommunication Network Design, and Relaxation Methods for infeasible linear systems.


Selin Damla Ahipaşaoğlu, Ph.D. Candidate

Title: A Modified Frank-Wolfe Algorithm for Computing Minimum-Area Enclosing Ellipsoidal Cylinders: Theory and Algorithms

School of Operations Research in Information Engineering at Cornell University, New York

Tuesday, February 10, 2009

ABSTRACT

Given an arbitrary set in the Euclidean space, we are interested in finding an ellipsoidal cylinder, centered at the origin such that its intersection with a certain subspace has minimum area. This problem is referred to as the Minimum-Area Enclosing Ellipoisal Cylinder (MAEC) problem. We discuss global and local convergence properties of the algorithm and present some computational results.

BIOGRAPHY

Selin Damla Ahipaşaoğlu is a fifth-year graduate student in the School of Operations Research and Information Engineering at Cornell University. She received her M.S. and B.S. degrees from Bilkent University in Turkey. Her research interests includ continuous optimization especially convex programming, optimal design, algorithms and matrix computations.


Guanghui Lan, Ph.D. Candidate

Title: Robust and Accelerated Stochastic Approximation Approaches for Stochastic Optimization

The H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology

Wednesday, February 4, 2009

ABSTRACT

Recognized as a powerful modeling technique in a diverse set of applications, stochastic optimization remains computationally challenging. In this talk we discuss some recent exciting advancement in stochastic approximation (SA) methods applied to stochastic convex optimization. We succeed in solving the problem by proposing an accelerated stochastic approximation method possessing this desired property. Some promising numerical results will also be presented for solving problems arising from financial risk management and network design under uncertainty.

BIOGRAPHY

Guanghui Lan is currently a Ph.D. candidate in the H. Milton Stewart School of Industrial and Systems Engineering at the Georgia Technical Institute. He obtained the Master of Science degree in Industrial Engineering from the University of Louisville in 2004. His research interests lies in stochastic/robust optimization, stochastic approximation, large-scale optimization, and their applications in finance, energy systems, logistics, etc.


Dr. Ignacio E. Grossmann, Rudolph R. and Florence Dean University Professor

Title: On the scope of Discrete-Continuous Optimization in Process Systems Engineering

Center for Advanced Process Decision-Making Department of Chemical Engineering - Carnegie Mellon University

Friday, January 16, 2009

ABSTRACT

In this talk we identify discrete and continuous optimization as a major capability that is required in the optimal design and operation of chemical plants and process supply chains. We first provide a brief overview of mixed-integer linear/nonlinear programming algorithms, followed by generalized disjunctive programming, which provides a modeling framework where models can be expressed through equations and symbolic logic relationships. We discuss approaches for developing tight relaxations of these problems, as well as for handling nonconvexities. We illustrate the application of these techniques in a variety of areas that include process separations, scheduling of batch processes, water networks, and supply chain optimization.

BIOGRAPHY

Ignacio E. Grossmann is the Rudolph R. and Florence Dean University Professor of Chemical Engineering, and former Department Head at Carnegie Mellon University. He obtained his B.S. degree in Chemical Engineering at the Universidad Iberoamericana, Mexico City, in 1974, and his M.S. and Ph.D. in Chemical Engineering at Imperial College in 1975 and 1977, respectively. He joined Carnegie Mellon in 1979.

The research interests of Ignacio Grossmann are in the areas of process synthesis, energy integration, process flexibility, planning and scheduling of batch and continuous processes, supply chain optimization, and mixed-integer and logic-based optimization. He has authored more than 300 papers, several monographs on design cases studies, and the textbook "Systematic Methods of Chemical Process Design."