Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

• 成果类型: Article
• 署名作者: Ben-Tal, Aharon; den Hertog, Dick; De Waegenaere, Anja; Melenberg, Bertrand; Rennen, Gijs
• 署名单位: Technion Israel Institute of Technology; Tilburg University; Tilburg University
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.1120.1641
• 发表日期: 2013
• 页码: 341-357
• 关键词: Robust Optimization; phi-divergence; goodness-of-fit statistics

摘要

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.