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Journal of Applied Mathematics
Volume 2014, Article ID 321010, 12 pages
http://dx.doi.org/10.1155/2014/321010
Research Article

A Regularization SAA Scheme for a Stochastic Mathematical Program with Complementarity Constraints

1Institute of ORCT, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
2School of Mathematics, Liaoning Normal University, Dalian 116029, China

Received 29 May 2013; Accepted 3 November 2013; Published 10 February 2014

Academic Editor: Song Cen

Copyright © 2014 Yu-xin Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

To reflect uncertain data in practical problems, stochastic versions of the mathematical program with complementarity constraints (MPCC) have drawn much attention in the recent literature. Our concern is the detailed analysis of convergence properties of a regularization sample average approximation (SAA) method for solving a stochastic mathematical program with complementarity constraints (SMPCC). The analysis of this regularization method is carried out in three steps: First, the almost sure convergence of optimal solutions of the regularized SAA problem to that of the true problem is established by the notion of epiconvergence in variational analysis. Second, under MPCC-MFCQ, which is weaker than MPCC-LICQ, we show that any accumulation point of Karash-Kuhn-Tucker points of the regularized SAA problem is almost surely a kind of stationary point of SMPCC as the sample size tends to infinity. Finally, some numerical results are reported to show the efficiency of the method proposed.