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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 816528, 15 pages
http://dx.doi.org/10.1155/2012/816528
Research Article

Expected Residual Minimization Method for a Class of Stochastic Quasivariational Inequality Problems

Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

Received 22 August 2012; Accepted 15 October 2012

Academic Editor: Xue-Xiang Huang

Copyright © 2012 Hui-Qiang Ma and Nan-Jing Huang. 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

We consider the expected residual minimization method for a class of stochastic quasivariational inequality problems (SQVIP). The regularized gap function for quasivariational inequality problem (QVIP) is in general not differentiable. We first show that the regularized gap function is differentiable and convex for a class of QVIPs under some suitable conditions. Then, we reformulate SQVIP as a deterministic minimization problem that minimizes the expected residual of the regularized gap function and solve it by sample average approximation (SAA) method. Finally, we investigate the limiting behavior of the optimal solutions and stationary points.