Models for minimax stochastic linear optimization problems with risk aversion

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Author(s)

  • Dimitris Bertsimas
  • Xuan Vinh Doan
  • Karthik Natarajan
  • Chung-Piaw Teo

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)580-602
Journal / PublicationMathematics of Operations Research
Volume35
Issue number3
Publication statusPublished - Aug 2010

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 productiontransportation 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. Copyright © 2010 INFORMS.

Research Area(s)

  • Minimax stochastic optimization, Moments, Risk aversion, Semidefinite optimization

Citation Format(s)

Models for minimax stochastic linear optimization problems with risk aversion. / Bertsimas, Dimitris; Doan, Xuan Vinh; Natarajan, Karthik; Teo, Chung-Piaw.

In: Mathematics of Operations Research, Vol. 35, No. 3, 08.2010, p. 580-602.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal