SPLITTING EXTRAGRADIENT-LIKE ALGORITHMS WITH BREGMAN DISTANCE FOR SOLVING EQUILIBRIUM PROBLEMS

In this paper, we propose splitting extragradient-like algorithms with Bregman distance for solving strongly pseudomonotone equilibrium problems where the underlying bifunction in the formulation of the equilibrium problem is the sum of two bifunctions. Under some suitable assumptions on the bifunction and the Bregman function, we prove the convergence of the sequences generated by the proposed algorithms to a solution of the equilibrium problem with rate of convergence being linear in the sense of Bregman distance. We also study the case when a part of the bifunction contains some errors. At the end of this paper, we provide some numerical examples to illustrate the proposed algorithms and their convergence results.