Stochastic methods based on Newton method to the stochastic variational inequality problem with constraint conditions

Two stochastic methods for solving a class of stochastic variational inequality problems (SVIPs) are presented, using the stochastic approximation (SA) method and the sample average approximation (SAA) method. They are constructed by SA and SAA methods based on the Newton method where the underlying functions are the expected values of stochastic functions. Local convergences are given under Lipschitzian conditions. Numerical experiments show that the proposed methods are efficient.