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

Indexed by:Journal Article

Date of Publication:2017-09-01

Journal:MATHEMATICAL PROGRAMMING

Included Journals:EI、SCIE、Scopus

Volume:165

Issue:1,SI

Page Number:433-470

ISSN:0025-5610

Key Words:Stochastic quasi-variational inequality; Quantitative stability analysis; Mathematical program with stochastic semidefinite constraints; Mathematical program with SQVIP constraints

Abstract: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.