Consistency analysis of a local Lipschitz homeomorphism of an SAA normal mapping for a parametric stochastic variational inequality

Indexed by:期刊论文

Journal:JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Included Journals:SCIE、Scopus

Volume:408

Issue:1

Page Number:306-317

ISSN No.:0022-247X

Key Words:Local Lipschitz homeomorphism; Sample average approximation; Parametric stochastic variational inequality; Stochastic mathematical program with complementarity constraints

Abstract:We investigate the consistency of a local Lipschitz homeomorphism of the normal mapping of a sample average approximation (SAA) parametric stochastic variational inequality. Since Thibault directional derivatives are unbounded, the notion of cosmic deviation is introduced to characterize the total outer limit of a sequence of Thibault directional derivatives of SAA mappings. We denionstrate that when the normal mapping of the original problem is locally Lipschitz homeomorphic, the normal mapping of the SAA problem is sufficient if the sample size is large enough. We use this result to develop the consistency of stationary points of the SAA estimator for a stochastic mathematical program with complementarity constraints. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.

Date of Publication:2013-12-01