@Article{JCM-42-390,
author = {Zhang , Ling and Xu , Lingling},
title = {Modified Stochastic Extragradient Methods for Stochastic Variational Inequality},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {2},
pages = {390--414},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2206-m2021-0195},
url = {http://global-sci.org/intro/article_detail/jcm/22886.html}
}