Concavity and efficient points of discrete distributions in probabilistic programming

Darinka Dentcheva, András Prékopa, Andrzej Ruszczyński

Research output: Contribution to journalArticlepeer-review

149 Scopus citations

Abstract

We consider stochastic programming problems with probabilistic constraints involving integer-valued random variables. The concept of a p-efficient point of a probability distribution is used to derive various equivalent problem formulations. Next we introduce the concept of r-concave discrete probability distributions and analyse its relevance for problems under consideration. These notions are used to derive lower and upper bounds for the optimal value of probabilistically constrained stochastic programming problems with discrete random variables. The results are illustrated with numerical examples.

Original languageEnglish
Pages (from-to)55-77
Number of pages23
JournalMathematical Programming
Volume89
Issue number1
DOIs
StatePublished - 2000

Keywords

  • Column generation
  • Discrete distributions
  • Generalized concavity
  • Probabilistic programming

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