Stability and sensitivity of optimization problems with first order stochastic dominance constraints

Darinka Dentcheva, René Henrion, Andrzej Ruszczyński

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31 Scopus citations

Abstract

We analyze the stability and sensitivity of stochastic optimization problems with stochastic dominance constraints of first order. We consider general perturbations of the underlying probability measures in the space of regular measures equipped with a suitable discrepancy distance. We show that the graph of the feasible set mapping is closed under rather general assumptions. We obtain conditions for the continuity of the optimal value and upper-semicontinuity of the optimal solutions, as well as quantitative stability estimates of Lipschitz type. Furthermore, we analyze the sensitivity of the optimal value and obtain upper and lower bounds for the directional derivatives of the optimal value. The estimates are formulated in terms of the dual utility functions associated with the dominance constraints.

Original languageEnglish (US)
Pages (from-to)322-337
Number of pages16
JournalSIAM Journal on Optimization
Volume18
Issue number1
DOIs
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science

Keywords

  • Chance constraints
  • Directional differentiability
  • Lipschitz stability
  • Metric regularity
  • Semi-infinite optimization
  • Stochastic ordering
  • Stochastic programming

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