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Indexed by:期刊论文

Date of Publication:2017-01-01

Journal:SIAM JOURNAL ON OPTIMIZATION

Included Journals:SCIE、EI

Volume:27

Issue:2

Page Number:784-816

ISSN No.:1052-6234

Key Words:distributionally robust chance constraint; approximation of ambiguity set; continuity of robust probability function; convergence analysis

Abstract:Convergence analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and the optimal solutions and research on this topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance constraints where the true probability distribution is unknown, but it is possible to construct an ambiguity set of probability distributions and the chance constraint is based on the most conservative selection of probability distribution from the ambiguity set. The convergence analysis focuses on impact of the variation of the ambiguity set on the optimal value and the optimal solutions. We start by deriving general convergence results under abstract conditions such as continuity of the robust probability function and uniform convergence of the robust probability functions and followed with detailed analysis of these conditions. Two sufficient conditions have been derived with one applicable to both continuous and discrete probability distribution and the other to continuous distribution. Case studies are carried out for ambiguity sets being constructed through moments and samples.