Stochastic Approximation Approaches To The Stochastic Variational Inequality Problem Based On Projection And Contraction Method

Variational inequality plays a vital role in transportation, finance and energy source. In our daily life there often encounter a lot of stochastic uncertainties which make important im-pact on some results such as needs, weather and so on. So it boosts the research of stochastic variational inequality. Projection and contraction method is an important algorithm for solving variational inequalities. It is easy to implement and can handle large scale problem. Professor He put forward some projection and contraction methods based on some basic properties of the projection operator. Stochastic approximation methods have been extensively studied in the lit-erature 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. This paper presents a new algorithm:stochastic approximation methods based on projection and contraction. Global convergence result of the proposed method is obtained under appropriate conditions. Some preliminary numerical results are reported for the examples that arise from the newsvendor pricing game.