Expected residual minimization method for stochastic variational inequality problems with nonlinear perturbations

In this paper, we consider stochastic affine variational inequality problems with nonlinear perturbation (for short, SVIPP). Firstly, we formulate SVIPP as an ERM problem that minimizes the expected residual of the so-called gap function. Furthermore, we study some properties of the ERM problem under some suitable conditions. By means of quasi-Monte Carlo method, we obtain a discrete approximation of ERM problem. Finally, we consider the convergence of optimal solutions and stationary points of the approximation problem as sample size increases.