Optimization with multivariate stochastic dominance constraints

Darinka Dentcheva, Andrzej Ruszczyński

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

We consider stochastic optimization problems where risk-aversion is expressed by a stochastic ordering constraint. The constraint requires that a random vector depending on our decisions stochastically dominates a given benchmark random vector. We identify a suitable multivariate stochastic order and describe its generator in terms of von Neumann-Morgenstern utility functions. We develop necessary and sufficient conditions of optimality and duality relations for optimization problems with this constraint. Assuming convexity we show that the Lagrange multipliers corresponding to dominance constraints are elements of the generator of this order, thus refining and generalizing earlier results for optimization under univariate stochastic dominance constraints. Furthermore, we obtain necessary conditions of optimality for non-convex problems under additional smoothness assumptions.

Original languageEnglish (US)
Pages (from-to)111-127
Number of pages17
JournalMathematical Programming
Volume117
Issue number1-2
DOIs
StatePublished - Mar 2009

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Keywords

  • Duality
  • Optimality
  • Risk
  • Stochastic order
  • Utility

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