The sample approximation method for the stochastic variational inequality problem with equality constraints

This paper presents a new method for solving stochastic variational inequality problems(SVIP), where the feasible set is the intersection of a simple set and polyhedron defined by a system of equality. We first formulate SVIP as an optimization problem that minimizes the expected residual of the so-called regularized gas function. Then we focus on the stochastic optimization problem. The method can be viewed as a combination of quasi-Monte Carlo and PSO. We test the new method, and the numerical results show that our approximate solution is very close to the true solution. Our new method is suitable for such class of variational inequality.