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

Davide la Torre, Franklin Mendivil

Research output: Contribution to journalArticle

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)1-8
Number of pages8
JournalJournal of the Operational Research Society
DOIs
Publication statusAccepted/In press - Jun 13 2017

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Sampling
Incomplete information
Uncertainty
Optimization problem
Law of large numbers
Central limit theorem
Expected value

Keywords

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

ASJC Scopus subject areas

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

Cite this

Stochastic linear optimization under partial uncertainty and incomplete information using the notion of probability multimeasure. / la Torre, Davide; Mendivil, Franklin.

In: Journal of the Operational Research Society, 13.06.2017, p. 1-8.

Research output: Contribution to journalArticle

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