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.