Journal of Nonlinear and Variational Analysis

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DOI: 10.23952/jnva.7.2023.6.08

Volume 7, Issue 6, 1 December 2023, Pages 995-1016

 

Abstract. In this paper, we investigate a stochastic approximation based algorithm for solving nonmonotone stochastic variational inequalities. Our algorithm combines the projection and contraction method with the inertial extrapolation technique. The self-adaptive step size sequence is generated by employing the Armijo’s line search rule. We also investigate the almost sure convergence property without using the prior knowledge of the Lipschitz constant of the involved operator in our algorithm. Theoretical results related to the convergence rate and the oracle complexity are provided under mild assumptions. Primary numerical experiments are presented to demonstrate the efficiency of the algorithm.

 

How to Cite this Article:
L. Liu, X. Qin, A stochastic projection and contraction algorithm with inertial effects for stochastic variational inequalities, J. Nonlinear Var. Anal. 7 (2023), 995-1016.