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

Abstract

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 $P$-function, stochastic $P_0$-function, and stochastic uniformly $P$-function. Furthermore, the conditions such that the function is a stochastic $P\left(P_0\right)$-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.