Title :
Stochastic Approximation Approaches to the Stochastic Variational Inequality Problem
Author :
Jiang, Houyuan ; Xu, Huifu
Author_Institution :
Judge Bus. Sch., Univ. of Cambridge, Cambridge
fDate :
7/1/2008 12:00:00 AM
Abstract :
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 for solving stochastic variational inequality problems (SVIP) where the underlying functions are the expected value of stochastic functions. Two types of methods are proposed: stochastic approximation methods based on projections and stochastic approximation methods based on reformulations of SVIP. Global convergence results of the proposed methods are obtained under appropriate conditions.
Keywords :
approximation theory; stochastic processes; variational techniques; first order derivatives; stochastic approximation approach; stochastic equations; stochastic optimization problem; stochastic variational inequality problem; Approximation methods; Books; Convergence; Equations; Game theory; Oligopoly; Optimization methods; Stochastic processes; Stochastic systems; Uncertainty; Projection method; simulation; stochastic approximation; stochastic complementarity problems; stochastic variational inequalities;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2008.925853