Quantitative Stability Analysis of Stochastic Quasi-Variational Inequality Problems and Applications

Jie Zhang(zhangjie04212001163.com)
Huifu Xu(H.Xusoton.ac.uk)
Li-wei Zhang(lwzhangdlut.edu.cn)

Abstract: We consider a parametric stochastic quasi-variational inequality problem (SQVIP for short) where the underlying normal cone is dened 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 eectively 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 semidenite constraints and a mathematical program with SQVIP constraints.

Keywords: Stochastic quasi-variational inequality, quantitative stability analysis, mathematical program with stochastic semidenite constraints, mathematical program with SQVIP constraints

Category 1: Stochastic Programming

Citation: J. Zhang, H. F. Xu and L. W. Zhang, Quantitative Stability Analysis of Stochastic Quasi-Variational Inequality Problems and Applications, Report, Institute of ORCT, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China. 01/2015

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Entry Submitted: 06/03/2015
Entry Accepted: 06/04/2015
Entry Last Modified: 06/03/2015

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