Modified Stochastic Extragradient Methods for Stochastic Variational Inequality

Modified Stochastic Extragradient Methods for Stochastic Variational Inequality

Year:    2024

Author:    Ling Zhang, Lingling Xu

Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 390–414

Abstract

In this paper, we consider two kinds of extragradient methods to solve the pseudo-monotone stochastic variational inequality problem. First, we present the modified stochastic extragradient method with constant step-size (MSEGMC) and prove the convergence of it. With the strong pseudo-monotone operator and the exponentially growing sample sequences, we establish the $R$-linear convergence rate in terms of the mean natural residual and the oracle complexity $O(1/\epsilon).$ Second, we propose a modified stochastic extragradient method with adaptive step-size (MSEGMA). In addition, the step-size of MSEGMA does not depend on the Lipschitz constant and without any line-search procedure. Finally, we use some numerical experiments to verify the effectiveness of the two algorithms.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2206-m2021-0195

Journal of Computational Mathematics, Vol. 42 (2024), Iss. 2 : pp. 390–414

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Stochastic variational inequality Pseudo-monotone Modified stochastic extragradient methods Adaptive step-size.

Author Details

Ling Zhang

Lingling Xu