On the Convergence of Coderivative of SAA Solution Mapping for a Parametric Stochastic Variational Inequality

Indexed by:期刊论文

Journal:SET-VALUED AND VARIATIONAL ANALYSIS

Included Journals:SCIE

Volume:20

Issue:1

Page Number:75-109

ISSN No.:1877-0533

Key Words:Coderivative; Sample average approximation; Parametric stochastic variational inequality; Lipschitz-like property; Stochastic bilevel program

Abstract:The aim of this paper is to investigate the convergence properties for Mordukhovich's coderivative of the solution map of the sample average approximation (SAA) problem for a parametric stochastic variational inequality with equality and inequality constraints. The notion of integrated deviation is introduced to characterize the outer limit of a sequence of sets. It is demonstrated that, under suitable conditions, both the cosmic deviation and the integrated deviation between the coderivative of the solution mapping to SAA problem and that of the solution mapping to the parametric stochastic variational inequality converge almost surely to zero as the sample size tends to infinity. Moreover, the exponential convergence rate of coderivatives of the solution maps to the SAA parametric stochastic variational inequality is established. The results are used to develop sufficient conditions for the consistency of the Lipschitz-like property of the solution map of SAA problem and the consistency of stationary points of the SAA estimator for a stochastic bilevel program.

Date of Publication:2012-03-01