ON STRONG CONVERGENCE THEOREMS FOR A VISCOSITY-TYPE TSENG’S EXTRAGRADIENT METHODS SOLVING QUASIMONOTONE VARIATIONAL INEQUALITIES

Abstract

The main goal of this research is to solve variational inequalities involving quasi-monotone operators in infinite-dimensional real Hilbert spaces numerically. The main advantage of these iterative schemes is the ease with which step size rules can be designed based on an operator explanation rather than the Lipschitz constant or another line search method. The proposed iterative schemes use a monotone and non-monotone step size strategy based on mapping (operator) knowledge as a replacement for the Lipschitz constant or another line search method. The strong convergences have been demonstrated to correspond well to the proposed methods and to settle certain control specification conditions. Finally, we propose some numerical experiments to assess the effectiveness and influence of iterative methods.