A self-adaptive inertial extragradient method for a class of split pseudomonotone variational inequality problems

Abstract In this article, we study a class of pseudomonotone split variational inequality problems (VIPs) with non-Lipschitz operator. We propose new inertial extragradient method self-adaptive step sizes for finding the solution to aforementioned problem in framework Hilbert spaces. Moreover, prove strong convergence result proposed algorithm without prior knowledge operator norm and under mild conditions on control parameters. The main advantages our are: obtained Lipschitz continuity condition often assumed by authors; minimized number projections per iteration compared related results literature; technique employed, which speeds up rate convergence; unlike several existing literature VIPs operators, does not require any linesearch its implementation. Finally, present numerical examples illustrate usefulness applicability algorithm.