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论文类型：期刊论文
发表时间：2013-12-01
发表刊物：JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
收录刊物：SCIE、Scopus
卷号：408
期号：1
页面范围：306-317
ISSN号：0022-247X
关键字：Local Lipschitz homeomorphism; Sample average approximation; Parametric stochastic variational inequality; Stochastic mathematical program with complementarity constraints
摘要：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.