BREGMAN SUBGRADIENT EXTRAGRADIENT METHOD WITH MONOTONE SELF-ADJUSTMENT STEPSIZE FOR SOLVING PSEUDO-MONOTONE VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS

Abstract

Using the concept of Bregman divergence, we propose a new sub-gradient extragradient method for approximating a common solution of pseudo-monotone and Lipschitz continuous variational inequalities and fixed pointproblem in real Hilbert spaces. The algorithm uses a new self-adjustmentrule for selecting the stepsize in each iteration and also, we prove a strongconvergence result for the sequence generated by the algorithm without priorknowledge of the Lipschitz constant. Finally, we provide some numerical ex-amples to illustrate the performance and accuracy of our algorithm in finiteand infinite dimensional spaces