Models for minimax stochastic linear optimization problems with risk aversion

Models for minimax stochastic linear optimization problems with risk aversion

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Article ID: iaor20106292
Volume: 35
Issue: 3
Start Page Number: 580
End Page Number: 602
Publication Date: Aug 2010
Journal: Mathematics of Operations Research
Authors: , , ,
Keywords: programming (semidefinite)
Abstract:

We propose a semidefinite optimization (SDP) model for the class of minimax two-stage stochastic linear optimization problems with risk aversion. The distribution of second-stage random variables belongs to a set of multivariate distributions with known first and second moments. For the minimax stochastic problem with random objective, we provide a tight SDP formulation. The problem with random right-hand side is NP-hard in general. In a special case, the problem can be solved in polynomial time. Explicit constructions of the worst-case distributions are provided. Applications in a production-transportation problem and a single facility minimax distance problem are provided to demonstrate our approach. In our experiments, the performance of minimax solutions is close to that of data-driven solutions under the multivariate normal distribution and better under extremal distributions. The minimax solutions thus guarantee to hedge against these worst possible distributions and provide a natural distribution to stress test stochastic optimization problems under distributional ambiguity.

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