A MODIFIED INERTIAL PARALLEL-TYPE SUBGRADIENT EXTRAGRADIENT METHOD FOR FINDING THE COMMON SOLUTION OF VARIATIONAL INEQUALITY PROBLEMS

Abstract

This paper introduces an inertial parallel-type subgradient extragradient algo-rithm, featuring inertial extrapolation terms and a self-adaptive step size rule, for finding acommon solution of variational inequality problems in real Hilbert spaces. We establish bothweak and strong convergence theorems for the proposed algorithm under suitable conditions.Furthermore, this method is extended to find a common element of the common solutionset of variational inequality problems and the xed point set of a quasi-nonexpansive map-ping. Finally, we present numerical experiments to illustrate the convergence behavior of ouralgorithm and demonstrate its advantages over several existing methods in the literature.