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Risk Aversion in Two-Stage Stochastic Integer Programs

Two-stage stochastic programs are deterministic equivalents to random optimization problems where decisions have to be taken stage-wise, i.e., before and after knowing the outcomes of random problem data. In particular, this entails non-anticipativity of first-stage decisions, meaning that decisions to be taken before knowing the random outcomes must not depend on the latter. Practical examples include production with random demand or network layout with random load. Traditional two-stage stochastic programs are based on optimizing the expectation of suitable random variables. In the talk we extend this framework to cover risk aversion. We discuss structural and algorithmic consequences of including different risk measures into purely expectation-based two-stage stochastic integer programs. Particular attention is paid to algorithmic issues where the risk measure determines whether or not block structures amenable to problem decomposition arise. Some first ideas to handle the different situations are presented. Numerical illustrations from scheduling a multiproduct chemical batch plant under uncertainty conclude the talk.
Type of Seminar:
Public Seminar
Prof. Rüdiger Schultz
Department of Mathematics, University of Duisburg-Essen
Nov 29, 2004   16:15

University of Zurich, Room K02-F-172
Contact Person:

Prof. M.Morari
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Biographical Sketch:
1982 Diplom in Mathematik, Spezialisierung: Optimierung, Humboldt-Universität zu Berlin //1985 Promotion (doctor rerum naturalium) in Mathematik, Humboldt-Universität zu Berlin, Titel der Dissertation: `Estimates for Kuhn-Tucker points of perturbed convex programs'// 1984 - 1993 wiss. Assistent, Institut für Mathematik, Humboldt-Universität zu Berlin// 1988 - 1989 Gastaufenthalt am Institut für Operations Research der Universität Zurich, Stipendium des Schweizer Bundes// 1993 - 1997 wiss. Angestellter, Abteilung Optimierung des Konrad-Zuse-Zentrums für Informationstechnik Berlin// 1995 Habilitation in Mathematik, Institut für Mathematik, Humboldt-Universität zu Berlin, Titel der Habilitationsschrift: `Structure and stability in two-stage stochastic programming'// 1997 - 1998 Universitäts-Professor (C3) für Diskreter Mathematik, Mathematisches Institut der Universität Leipzig// 1998 - Universitäts-Professor (C4) für Diskrete Mathematik und Optimierung, Institut für Mathematik, Gerhard-Mercator Universität Duisburg