TY - JOUR
T1 - Modified Stochastic Extragradient Methods for Stochastic Variational Inequality
AU - Zhang , Ling
AU - Xu , Lingling
JO - Journal of Computational Mathematics
VL - 2
SP - 390
EP - 414
PY - 2024
DA - 2024/01
SN - 42
DO - http://doi.org/10.4208/jcm.2206-m2021-0195
UR - https://global-sci.org/intro/article_detail/jcm/22886.html
KW - Stochastic variational inequality, Pseudo-monotone, Modified stochastic extragradient methods, Adaptive step-size.
AB - <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>