Stochastic Systems

Solving variational inequalities with stochastic mirror-prox algorithm

Anatoli Juditsky, Arkadi Nemirovski, and Claire Tauvel

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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.

Article information

Stoch. Syst., Volume 1, Number 1 (2011), 17-58.

First available in Project Euclid: 24 February 2014

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Zentralblatt MATH identifier

Primary: 90C15: Stochastic programming 65K10: Optimization and variational techniques [See also 49Mxx, 93B40]
Secondary: 90C47: Minimax problems [See also 49K35]

Variational inequalities with monotone operators stochastic convex-concave saddle-point problem large scale stochastic approximation reduced complexity algorithms for convex optimization


Juditsky, Anatoli; Nemirovski, Arkadi; Tauvel, Claire. Solving variational inequalities with stochastic mirror-prox algorithm. Stoch. Syst. 1 (2011), no. 1, 17--58. doi:10.1214/10-SSY011.

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