Optimization with multivariate stochastic dominance constraints

Darinka Dentcheva, Eli Wolfhagen

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We consider risk-averse stochastic optimization problems with a risk-shaping constraint in the form of a multivariate stochastic order constraint. The constraint requires that a random vector depending on our decisions stochastically dominates a given benchmark random vector in the sense of the linear stochastic dominance of second order. We refine the optimality conditions for problems with this type of constraint by using atomic measures. Additionally, we propose a primal and a dual numerical method for solving the problem and formulate sufficient conditions for their convergence. Numerical experience and comparisons to other approaches are provided.

Original languageEnglish
Pages (from-to)564-588
Number of pages25
JournalSIAM Journal on Optimization
Volume25
Issue number1
DOIs
StatePublished - 2015

Keywords

  • Bundle methods
  • DC optimization
  • Duality
  • Multivariate dominance relation
  • Risk
  • Stochastic order

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