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Journal of Applied Mathematics
Volume 2013, Article ID 497586, 7 pages
Research Article

Properties of Expected Residual Minimization Model for a Class of Stochastic Complementarity Problems

1School of Mathematics, Liaoning University, Liaoning 110036, China
2School of Sciences, Shenyang University, Liaoning 110044, China

Received 31 January 2013; Revised 10 May 2013; Accepted 14 May 2013

Academic Editor: Farhad Hosseinzadeh Lotfi

Copyright © 2013 Mei-Ju Luo and Yuan Lu. 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.


Expected residual minimization (ERM) model which minimizes an expected residual function defined by an NCP function has been studied in the literature for solving stochastic complementarity problems. In this paper, we first give the definitions of stochastic -function, stochastic -function, and stochastic uniformly -function. Furthermore, the conditions such that the function is a stochastic -function are considered. We then study the boundedness of solution set and global error bounds of the expected residual functions defined by the “Fischer-Burmeister” (FB) function and “min” function. The conclusion indicates that solutions of the ERM model are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in stochastic complementarity problems. On the other hand, we employ quasi-Monte Carlo methods and derivative-free methods to solve ERM model.