Quantitative stability analysis of stochastic quasi-variational inequality problems and applications

• 成果类型: Article
• 署名作者: Zhang, Jie; Xu, Huifu; Zhang, Liwei
• 署名单位: Liaoning Normal University; University of Southampton; Dalian University of Technology; Dalian University of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-017-1116-9
• 发表日期: 2017
• 页码: 433-470
• 关键词: generalized equations; sensitivity-analysis; complementarity constraints; mathematical programs; error-bounds; nash games; optimization

摘要

We consider a parametric stochastic quasi-variational inequality problem (SQVIP for short) where the underlying normal cone is defined over the solution set of a parametric stochastic cone system. We investigate the impact of variation of the probability measure and the parameter on the solution of the SQVIP. By reformulating the SQVIP as a natural equation and treating the orthogonal projection over the solution set of the parametric stochastic cone system as an optimization problem, we effectively convert stability of the SQVIP into that of a one stage stochastic program with stochastic cone constraints. Under some moderate conditions, we derive Holder outer semicontinuity and continuity of the solution set against the variation of the probability measure and the parameter. The stability results are applied to a mathematical program with stochastic semidefinite constraints and a mathematical program with SQVIP constraints.