PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Solving variational inequalities with Stochastic Mirror-Prox algorithm
A. Juditsky and A. Nemirovski
SIAM J. Optimization 2008.


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.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:5196
Deposited By:Anatoli Iouditski
Deposited On:24 March 2009