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2011 Solving variational inequalities with stochastic mirror-prox algorithm
Anatoli Juditsky, Arkadi Nemirovski, Claire Tauvel
Stoch. Syst. 1(1): 17-58 (2011). DOI: 10.1214/10-SSY011

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.

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Anatoli Juditsky. Arkadi Nemirovski. Claire Tauvel. "Solving variational inequalities with stochastic mirror-prox algorithm." Stoch. Syst. 1 (1) 17 - 58, 2011. https://doi.org/10.1214/10-SSY011

Information

Published: 2011
First available in Project Euclid: 24 February 2014

zbMATH: 1291.49006
MathSciNet: MR2948917
Digital Object Identifier: 10.1214/10-SSY011

Subjects:
Primary: 65K10, 90C15
Secondary: 90C47

Rights: Copyright © 2011 INFORMS Applied Probability Society

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Vol.1 • No. 1 • 2011
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