Víctor Zavala

University of Wisconsin, USA

“Stochastic Programming: Formulations, Algorithms, and Applications”

Resumen: This short course is targeted towards graduate students and practitioners interested in learning how to formulate, analyze, and solve stochastic programming problems. The course provides a review of probability and optimization concepts and covers different problem classes that include risk metrics, probabilistic constraints, and (partial) differential equations. The course also explores conceptual connections with non-smooth and mixed-integer optimization that facilitates modeling and analysis. Algorithms and software tools for the solution of continuous and mixed-integer formulations in parallel computers are also discussed. Numerical examples implemented in the open-source Julia programming language are provided. Finally, real applications are discussed to demonstrate the scope of the concepts and tools.

Bio: Victor M. Zavala is the Richard H. Soit Assistant Professor in the Department of Chemical and Biological Engineering at the University of Wisconsin-Madison. Before joining UW-Madison, he was a computational mathematician in the Mathematics and Computer Science Division at Argonne National Laboratory. He holds a B.Sc. degree from Universidad Iberoamericana and a Ph.D. degree from Carnegie Mellon University, both in chemical engineering.  He is on the editorial board of the Journal of Process Control and Mathematical Programming Computation. His research interests are in the areas of mathematical modeling of energy systems, high-performance computing, optimization under uncertainty, and model predictive control.


Monique Guignard

University of Pensylvania, Philadelphia

“Lagrangean relaxation: what it is, when and how to use it, examples.”

Resumen: Lagrangean relaxation (LR) is used primarily in integer programming. It does not usually solve problems by itself, but it may allow the user (1) to compute strong bounds on the optimal value and (2) in many cases, to obtain good feasible solutions via ad-hoc heuristics. If successful, this will provide a bracket on the optimum. We will first concentrate on linear problems. The Integrality Property is a necessary condition for the LR bound to possibly dominate the LP bound. After a brief survey of the most common iterative methods for computing a Lagrangean bound, we will refer to some more sophisticated approaches that might be needed for hard-to-converge cases. If an LR model satisfies the Integer Linearization Property (ILP), a considerable speed-up in its solution may be achievable as it will decompose into much smaller and simpler subproblems. It is therefore very important to recognize the ILP when present. We will also define Lagrangean Decomposition (LD) and Lagrangean Substitution (LS), with examples that show the great variety of potential Lagrangean schemes. Finally we will describe recent uses of Lagrangean relaxation in the context of reformulation and linearization (RLT) of quadratic 0-1 problems with linear constraints. We will present examples for which stronger bounds have been obtained much faster, and also for much larger instances, than previously achieved.

Bio: Monique Guignard is Professor at the Department of Operations, Information and Decisions of the Wharton School, University of Pennsylvania. She holds a Thèse de Doctorat ès-Sciences Mathématiques, Très Honorable avec Félicitations du Jury, 1980 at the Université des Sciences et Techniques de Lille, France, where she worked with Professeur Pierre Huard. She has been Visiting Professor at the Université de Paris-Orsay, Université de Valenciennes, Université de Paris-Nord, and Université de Versailles, Fudan University in Shanghai, China, the University of Chile in Santiago and Universidad de Concepción. Her interest is in Large Scale Optimization and Integer Programming, a field in which she has made significant methodological and practical contributions, particularly by using Lagrangean approaches. She has several publications in the most prestigious journals of the field, of which she has also served as editor or co-editor. She was awarded the IFORS Distinguished Lecturer title at the 2016 CLAIO in Santiago, Chile.

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