Modified Bregman extragradient algorithm for equilibrium problems in Banach spaces

Abstract

This paper introduces a modified Bregman extragradient algorithm designed to solve pseudomonotone equilibrium problems in a real reflexive Banach space. The algorithm guarantees weak convergence under mild assumptions and establishes strong convergence under additional conditions. In our proposed algorithm, we utilize two parameters with the Bregman distance and a non-monotonic step size, which is independent of the Bregman Lipschitz constant, to enhance the algorithm's effectiveness. Furthermore, numerical experiments are conducted to validate the performance of the proposed algorithm, demonstrating significant improvements in efficiency compared to traditional algorithms in similar settings.