An extension of hybrid method without extrapolation step to equilibrium problems

Abstract

In this paper, we introduce a new hybrid algorithm for solving equilibrium problems. The algorithm combines the extragradient method and the hybrid (outer approximation) method. In this algorithm, only an optimization program is solved at each iteration without the extra-steps like as in the extragradient method and the Armijo linesearch method. A specially constructed half-space in the hybrid method is the reason for the absence of an optimization program in our algorithm. The strong convergence theorem is established and several numerical experiments are implemented to illustrate the convergence of the algorithm and compare it with others.