The Ishikawa Subgradient Extragradient Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces
Manh Hy Duc, Ha Nguyen Thanh, Thanh Tran Thi Huyen, Bui Van Dinh · Numerical Functional Analysis and Optimization · 2020
In this paper, we introduce a novel algorithm for finding a common point of the solution set of a class of equilibrium problems involving pseudo-monotone bifunctions and satisfying the Lipschitz-type condition and the set of fixed points of a quasi-nonexpansive in a real Hilbert space. This algorithm can be considered as a combination of the subgradient extragradient method for equilibrium problems and the Ishikawa method for fixed point problems. The strong convergence of the iterates generated by the proposed method is obtained under the main assumptions that the fixed-point mapping is demiclosed at 0 and Lipschitz-type constant of the cost bifunction is unknown. Some numerical examples are implemented to show the computational efficiency of the proposed algorithm.