Robust solutions of optimization problems affected by uncertain probabilities

Research output: Contribution to journalArticleScientificpeer-review

Abstract

In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences (for example, chi-squared, Hellinger, Kullback–Leibler). We show how uncertainty regions based on Φ-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 Φ-divergence uncertainty is tractable for most of the choices of Φ 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.
Original languageEnglish
Pages (from-to)341-357
JournalManagement Science
Volume59
Issue number2
Publication statusPublished - 2013

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Uncertainty
Optimization problem
Divergence
Finance
Expected utility
Asset pricing
Random variables
Newsvendor
Confidence set
Inventory control

Cite this

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title = "Robust solutions of optimization problems affected by uncertain probabilities",
abstract = "In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences (for example, chi-squared, Hellinger, Kullback–Leibler). We show how uncertainty regions based on Φ-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 Φ-divergence uncertainty is tractable for most of the choices of Φ 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.",
author = "A. Ben-Tal and {den Hertog}, D. and {De Waegenaere}, A.M.B. and B. Melenberg and G. Rennen",
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journal = "Management Science",
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Robust solutions of optimization problems affected by uncertain probabilities. / Ben-Tal, A.; den Hertog, D.; De Waegenaere, A.M.B.; Melenberg, B.; Rennen, G.

In: Management Science, Vol. 59, No. 2, 2013, p. 341-357.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Robust solutions of optimization problems affected by uncertain probabilities

AU - Ben-Tal, A.

AU - den Hertog, D.

AU - De Waegenaere, A.M.B.

AU - Melenberg, B.

AU - Rennen, G.

N1 - Appeared earlier as CentER Discussion Paper 2011-061

PY - 2013

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N2 - In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences (for example, chi-squared, Hellinger, Kullback–Leibler). We show how uncertainty regions based on Φ-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 Φ-divergence uncertainty is tractable for most of the choices of Φ 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.

AB - In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ-divergences (for example, chi-squared, Hellinger, Kullback–Leibler). We show how uncertainty regions based on Φ-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 Φ-divergence uncertainty is tractable for most of the choices of Φ 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.

M3 - Article

VL - 59

SP - 341

EP - 357

JO - Management Science

JF - Management Science

SN - 0025-1909

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