Inertial Bregman Subgradient Extragradient Methods for Solving Pseudomonotone Equilibrium and Fixed Point Problems in Reflexive Banach Spaces

Abstract

This paper proposes an inertial Bregman subgradient extragradient algorithm for approximating a common solution of pseudomonotone equilibrium problems and fixed point problems associated with Bregman relatively nonexpansive mappings in reflexive Banach spaces. The proposed method incorporates an inertial extrapolation step into the Bregman subgradient extragradient framework and employs a self-adaptive stepsize rule. Under suitable assumptions on the bifunction and the underlying Banach space, strong convergence of the generated sequence to a common solution is established. Several consequences of the main theorem are also derived. Numerical experiments are presented to illustrate the convergence behavior and effectiveness of the proposed algorithm.