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