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  • 张立卫 ( 教授 )

    的个人主页 http://faculty.dlut.edu.cn/1992011039/en/index.htm

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QUANTITATIVE STABILITY ANALYSIS FOR DISTRIBUTIONALLY ROBUST OPTIMIZATION WITH MOMENT CONSTRAINTS

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论文类型:期刊论文
第一作者:Zhang, Jie
通讯作者:Zhang, J (reprint author), Liaoning Normal Univ, Sch Math, Dalian 116029, Peoples R China.
合写作者:Xu, Huifu,Zhang, Liwei
发表时间:2016-01-01
发表刊物:SIAM JOURNAL ON OPTIMIZATION
收录刊物:SCIE、EI
卷号:26
期号:3
页面范围:1855-1882
ISSN号:1052-6234
关键字:distributionally robust optimization; moment conditions with cone constraints; Holder continuity of the optimal value function; outer semicontinuity of the set of optimal solutions; quantitative stability analysis
摘要:In this paper we consider a broad class of distributionally robust optimization (DRO) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is defined through parametric moment conditions with generic cone constraints. Under some moderate conditions, including Slater-type conditions of a cone constrained moment system and Holder continuity of the underlying random functions in the objective and moment conditions, we show local Holder continuity of the optimal value function of the inner maximization problem with respect to (w.r.t.) the decision vector and other parameters in moment conditions, and local Holder continuity of the optimal value of the whole minimax DRO w.r.t. the parameter. Moreover, under the second order growth condition of the Lagrange dual of the inner maximization problem, we demonstrate and quantify the outer semicontinuity of the set of optimal solutions of the minimax DRO w.r.t. variation of the parameter. Finally, we apply the established stability results to two particular classes of DRO problems.

 

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