@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 = {
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.
}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2206-m2021-0195}, url = {http://global-sci.org/intro/article_detail/jcm/22886.html} }