New inertial algorithm for a class of equilibrium problems

Abstract

The article introduces a new algorithm for solving a class ofequilibrium problems involving strongly pseudomonotone bifunctions with Lipschitz-type condition. We describe how to incorporate the proximal-like regularized technique with inertial effects. The main novelty of the algorithm is that it can be done without previously knowing the information on the strongly pseudomonotone and Lipschitz-type constants of cost bifunction. A reasonable explain for this is that the algorithm uses a sequence of stepsizes which is diminishing and non-summable. Theorem of strong convergence is proved. In the case, when the information on the modulus of strong pseudomonotonicity and Lispchitz-type constant is known,the rate of linear convergence of the algorithm has been established. Several of numerical experiments are performed to illustrate the convergence of the algorithm and also compare it with other algorithms.