期刊
MATHEMATICS OF OPERATIONS RESEARCH
卷 35, 期 3, 页码 580-602出版社
INFORMS
DOI: 10.1287/moor.1100.0445
关键词
minimax stochastic optimization; moments; risk aversion; semidefinite optimization
资金
- Department of Mathematics, National University of Singapore
- Singapore-MIT Alliance
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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