Method of weighted expected residual for solving stochastic variational inequality problems

This paper is concerned in constructing a deterministic model for the stochastic affine variational inequality problems with nonlinear perturbation (for short, SVIPP) based on the convex combined expectations of the least absolute deviation and least squares about the so-called regularized gap function. We formulate SVIPP as a weighted expected residual minimization problem (in short, WERM). Some properties of the WERM problem are derived under suitable conditions. Moreover, we obtain a discrete approximation of WERM problem by applying the quasi-Monte Carlo method. The limiting behavior of optimal solutions and stationary points of the approximation problem are analyzed as well.