Name
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1287/moor.1100.0445 | MATHEMATICS OF OPERATIONS RESEARCH |
Keywords | DocType | Volume |
minimax stochastic optimization,moments,risk aversion,semidefinite optimization | Journal | 35 |
Issue | ISSN | Citations |
3 | 0364-765X | 50 |
PageRank | References | Authors |
1.98 | 14 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dimitris J. Bertsimas | 1 | 4513 | 365.31 |
| Xuan Vinh Doan | 2 | 80 | 7.42 |
| Karthik Natarajan | 3 | 407 | 31.52 |
| Chung-Piaw Teo | 4 | 864 | 69.27 |