An inertial hybrid extragradient-viscosity method for solving quasimonotone variational inequalities

Abstract

This research aims to solve variational inequalities involving quasimonotone operators in infinite-dimensional real Hilbert spaces numerically. The simplicity of defining step size rules using an operator explanation is the fundamental advantage of iterative strategies, rather than the Lipschitz constant or another line search method. The proposed iterative techniques replace a monotone and non-monotone step size strategy based on mapping knowledge for the Lipschitz constant or an alternative line search algorithm. The strong convergences have been proven to be consistent with the offered methodologies and to resolve specific control specification limitations. Finally, we present numerical experiments that assess the efficacy and impact of iterative approaches.