Solving variational inequalities with Stochastic Mirror-Prox algorithm

Date
Authors
Juditsky, Anatoli
Nemirovskii, Arkadii S.
Tauvel, Claire
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
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 Feasability problem and Eigenvalue minimization.
Keywords
Mathematics - Optimization and Control, Mathematics - Statistics Theory
Citation
Collections