Solving variational inequalities with Stochastic Mirror-Prox algorithm

Abstract

In this paper we consider iterative methods for stochastic variational inequalities (s.v.i.) with monotone operators. Our basic assumption is that the operator possesses both smooth and nonsmooth components. Further, only noisy observations of the problem data are available. We develop a novel Stochastic Mirror-Prox (SMP) algorithm for solving s.v.i. and show that with the convenient stepsize strategy it attains the optimal rates of convergence with respect to the problem parameters. We apply the SMP algorithm to Stochastic composite minimization and describe particular applications to Stochastic Semidefinite Feasibility problem and deterministic Eigenvalue minimization. AMS 2000 subject classifications: Primary 90C15, 65K10; secondary 90C47.

01020302008200920102011201220132014201520162017
Citations per Year

86 Citations

Semantic Scholar estimates that this publication has 86 citations based on the available data.

See our FAQ for additional information.

Cite this paper

@inproceedings{Juditsky2008SolvingVI, title={Solving variational inequalities with Stochastic Mirror-Prox algorithm}, author={Anatoli Juditsky and Arkadi Nemirovski and Claire Tauvel}, year={2008} }