Convergence of relaxed inertial methods for equilibrium problems

In this paper, we first introduce a relaxed inertial algorithm for solving a pseudomonotone equilibrium problem with a Lipschitz-type condition in a Hilbert space. The algorithm is constructed around the proximal-like mapping and the inertial technique. The weak convergence of the algorithm is proved under some mild conditions. We also present a modified version of the first algorithm which can be implemented more easily without the prior knowledge of the Lipschitz-type constant of bifunction. Finally, several experiments are performed to illustrate the numerical behavior of the new algorithms, and also to show their computational efficiency over others.