A simple proximal algorithm based on the golden ratio for equilibrium problem on Hadamard manifolds

Abstract In this paper, we propose a simple proximal method which is combined with the inertial and golden ratio technique as extrapolation methods for approximating a solution to the equilibrium problem. The proposed method is self-adaptive such that its execution does not depend on the knowledge of the Lipschitz condition of the associated pseudomonotone cost operator. Under mild and standard assumptions on the control parameters, we showed that the sequence of iterates generated by this method converges to a solution of the problem. Assuming that the cost operator is strongly pseudomonotone, we prove that the sequence of iterates converge R -linearly to a solution of the EP. To show the numerical efficiency of this proposed method, we displayed some numerical experiments.