Golden ratio algorithms for solving equilibrium problems in Hilbert spaces

Abstract

In this paper, we design a new iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert spaces. The advantage of our algorithm is that it requires only one strongly convex programming problem at each iteration. Under suitable conditions we establish the strong and weak convergence of the proposed algorithm. The results presented in the paper extend and improve some recent results in the literature. The performances and comparisons with some existing methods are presented through numerical examples.