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 stochasticP-function, stochasticP0-function, and stochastic uniformlyP-function. Furthermore, the conditions such that the function is a stochasticPP0-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.

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We present a new method for solving the box-constrained stochastic linear variational inequality problem with three special types of uncertainty sets. Most previous methods, such as the expected value and expected residual minimization, need the probability distribution information of the stochastic variables. In contrast, we give the robust reformulation and reformulate the problem as a quadratically constrained quadratic program or convex program with a conic quadratic inequality quadratic program, which is tractable in optimization theory.