Dual methods for probabilistic optimization problems

Darinka Dentcheva, Bogumila Lai, Andrzej Ruszczyński

Research output: Contribution to journalArticlepeer-review

37 Scopus citations

Abstract

We consider nonlinear stochastic optimization problems with probabilistic constraints. The concept of a p-efficient point of a probability distribution is used to derive equivalent problem formulations, and necessary and sufficient optimality conditions. We analyze the dual functional and its subdifferential. Two numerical methods are developed based on approximations of the p-efficient frontier. The algorithms yield an optimal solution for problems involving r-concave probability distributions. For arbitrary distributions, the algorithms provide upper and lower bounds for the optimal value and nearly optimal solutions. The operation of the methods is illustrated on a cash matching problem with a probabilistic liquidity constraint.

Original languageEnglish
Pages (from-to)331-346
Number of pages16
JournalMathematical Methods of Operations Research
Volume60
Issue number2
DOIs
StatePublished - Oct 2004

Keywords

  • Convex programming
  • Duality
  • Liquidity constraints
  • Probabilistic constraints
  • Stochastic programming

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