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论文类型：期刊论文

发表时间：2020-05-15

发表刊物：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

收录刊物：SCIE

卷号：485

期号：2

ISSN号：0022-247X

关键字：Stochastic programming; Linear semi-definite programming; Probability metric; Quantitative stability analysis; Distributionally robust optimization

摘要：In this paper, we study a distributionally robust risk optimization (DRRO) problem where the information on the probability distribution of the underlying random variables is incomplete. But it is possible to use partial information to construct an ambiguity set of probability distributions. In some cases, decision vector x may have a direct impact on the likelihood of the underlying random events that occur after the decision is taken, which motivates us to propose an ambiguity set to be parametric and decision-dependent. To conduct quantitative stability analysis of the optimal value function and the optimal solution mapping of the DRRO problem, we derive error bounds results for the parametrized ambiguity set under the total variation metric and investigate Lipschitz continuity of the objective function of the DRRO problem under some conditions. As an application, we demonstrate that the two-stage stochastic linear semi-definite programs satisfy these conditions and then apply results obtained to it. (C) 2019 Elsevier Inc. All rights reserved.