Modified inertial subgradient extragradient algorithms for pseudomonotone equilibrium problems with the constraint of nonexpansive mappings

Abstract

In this paper, we introduce the modified inertial subgradient extragradient algorithms for solving the pseudomonotone equilibrium problems with the constraint of nonexpansive mappings. In our algorithms, the subgradient projection onto some constructible half-space is used in place of the second minimization problem over a closed convex set, and a new approach for attaining the step-size is provided. Strong convergence theorems are established in the framework of Hilbert spaces.