A new weak convergence non-monotonic self-adaptive iterative scheme for solving equilibrium problems

A number of methods have been proposed to solve the equilibrium problems, one of which is an extragradient method that is particularly interesting and effective. In this paper, we introduce a modified subgradient extragradient method to solve the equilibrium problems in a real Hilbert space. The proposed method uses a non-monotonic step size rule based on local bi-function information instead of its Lipschitz-type constant or other line search method and is capable of solving pseudo-monotone equilibrium problems. Our method only needs to solve a strongly convex programming problem per iteration. Applications of the designed algorithm are presented in order to solve fixed-point problems and variational inequalities. Finally, several computational experiments are studied to confirm the effectiveness of the proposed method. The results of our study include many similar literature studies and detailed numerical studies also show their potential usefulness.