张立卫Liwei Zhang

(教授)

 博士生导师  硕士生导师
学位:博士
性别:男
毕业院校:大连理工大学
所在单位:数学科学学院
电子邮箱:lwzhang@dlut.edu.cn

论文成果

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CONVERGENCE ANALYSIS FOR MATHEMATICAL PROGRAMS WITH DISTRIBUTIONALLY ROBUST CHANCE CONSTRAINT

发表时间:2019-03-12 点击次数:

论文名称:CONVERGENCE ANALYSIS FOR MATHEMATICAL PROGRAMS WITH DISTRIBUTIONALLY ROBUST CHANCE CONSTRAINT
论文类型:期刊论文
第一作者:Guo, Shaoyan
通讯作者:Guo, SY (reprint author), Univ Southampton, Sch Math Sci, Southampton SO17 1BJ, Hants, England.; Guo, SY (reprint author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.
合写作者:Xu, Huifu,Zhang, Liwei
发表刊物:SIAM JOURNAL ON OPTIMIZATION
收录刊物:SCIE、EI
卷号:27
期号:2
页面范围:784-816
ISSN号:1052-6234
关键字:distributionally robust chance constraint; approximation of ambiguity set; continuity of robust probability function; convergence analysis
摘要: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.
发表时间:2017-01-01