Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

Aharon Ben-Tal (), Dick den Hertog (), Anja De Waegenaere (), Bertrand Melenberg () and Gijs Rennen ()
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Aharon Ben-Tal: Department of Industrial Engineering and Management, Technion-Israel Institute of Technology, Haifa 32000, Israel; and CentER, Tilburg University, 5000 LE Tilburg, The Netherlands
Dick den Hertog: Department of Econometrics and Operations Research, Tilburg University, 5000 LE Tilburg, The Netherlands
Bertrand Melenberg: Department of Econometrics and Operations Research, Tilburg University, 5000 LE Tilburg, The Netherlands
Gijs Rennen: Department of Econometrics and Operations Research, Tilburg University, 5000 LE Tilburg, The Netherlands

Management Science, 2013, vol. 59, issue 2, 341-357

Abstract: In this paper we focus on robust linear optimization problems with uncertainty regions defined by [phi]-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on [phi]-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with [phi]-divergence uncertainty is tractable for most of the choices of [phi] typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach. This paper was accepted by Gérard P. Cachon, optimization.

Keywords: robust optimization; [phi]-divergence; goodness-of-fit statistics (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (145)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:59:y:2013:i:2:p:341-357

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