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Stability and sensitivity of stochastic dominance constrained optimization models
Please always quote using this URN:urn:nbn:de:0296-matheon-11625
- We consider convex optimization problems with $k$th order stochastic dominance constraints for $k\ge 2$. We discuss distances of random variables that are relevant for the dominance relation and establish quantitative stability results for optimal values and solution sets in terms of a suitably selected probability metrics.Moreover, we provide conditions ensuring that the optimal value function is Hadamard directionally differentiable. Finally, we discuss some implications of the results for empirical (Monte Carlo, sample average) approximations of dominance constrained optimization models.
Author: | Darinka Dentcheva, Werner Roemisch |
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URN: | urn:nbn:de:0296-matheon-11625 |
Referee: | Fredi Tröltzsch |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2012/08/02 |
Release Date: | 2012/08/02 |
Tag: | |
Institute: | Humboldt-Universität zu Berlin |
MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C15 Stochastic programming |
Preprint Number: | 978 |