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Title: Models for minimax stochastic linear optimization problems with risk aversion
Authors: Bertsimas, D.
Doan, X.V.
Natarajan, K.
Teo, C.-P. 
Keywords: Minimax stochastic optimization
Risk aversion
Semidefinite optimization
Issue Date: 2010
Citation: Bertsimas, D., Doan, X.V., Natarajan, K., Teo, C.-P. (2010). Models for minimax stochastic linear optimization problems with risk aversion. Mathematics of Operations Research 35 (3) : 580-602. ScholarBank@NUS Repository.
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.
Source Title: Mathematics of Operations Research
ISSN: 0364765X
DOI: 10.1287/moor.1100.0445
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