Stochastic linear optimization under partial uncertainty and incomplete information using the notion of probability multimeasure. Issue 10 (3rd October 2018)

• Record Type: Journal Article
• Authors: La Torre, Davide; Mendivil, Franklin
• Is Part Of: Journal of the Operational Research Society. Volume 69:Issue 10(2018)
• Page Start: 1549
• Page End: 1556
• Publication Date: 2018-10-03
• Subjects: Stochastic linear optimization -- deterministic equivalent problem -- set-valued optimization -- probability multimeasure; Operations research -- Periodicals; 658.4034
• DOI: 10.1057/s41274-017-0249-9
• Languages: English
• ISSNs: 0160-5682

Abstract

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.