Stochastic linear optimization under partial uncertainty and incomplete information using the notion of probability multimeasure

Davide La Torre, Franklin Mendivil

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We consider a scalar stochastic linear optimization problem subject to linear constraints. We introduce the notion of deterministic equivalent formulation when the underlying probability space is equipped with a probability multimeasure. The initial problem is then transformed into a set-valued optimization problem with linear constraints. We also provide a method for estimating the expected value with respect to a probability multimeasure and prove extensions of the classical strong law of large numbers, the Glivenko–Cantelli theorem, and the central limit theorem to this setting. The notion of sampling with respect to a probability multimeasure and the definition of cumulative distribution multifunction are also discussed. Finally, we show some properties of the deterministic equivalent problem.

Original languageEnglish
Pages (from-to)1549-1556
Number of pages8
JournalJournal of the Operational Research Society
Volume69
Issue number10
DOIs
Publication statusPublished - Oct 3 2018

Keywords

  • Stochastic linear optimization
  • deterministic equivalent problem
  • probability multimeasure
  • set-valued optimization

ASJC Scopus subject areas

  • Management Information Systems
  • Strategy and Management
  • Management Science and Operations Research
  • Marketing

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