Stochastic Methods Based On Newton Method To The Stochastic Variational Inequality Problem

Stochastic approximation methods have been extensively studied in the literature for solving systems of stochastic equations and stochastic optimization problems where function values and first order derivatives are not observable but can be approximated through simulation. In this paper, we investigate stochastic approximation methods based on Newton for solving stochastic variational inequality problems (SVIP). We study the stochastic approximation method based on Newton’s method which only require the ob-jective function is locally Lipschitz. We present the corresponding algorithm and prove its local convergence. We give the Newtonian approximation sequence which applied to the objective function.