Weak and Strong Convergence of Subgradient Extragradient Methods for Pseudomonotone Equilibrium Problems

Abstract

Abstract. In this paper, we introduce three subgradient extragradient algorithms for solving pseudomonotone equilibrium problems. The paper originates from the subgradient extragradient algorithm for variational inequalities and the extragradient method for pseudomonotone equilibrium problems in which we have to solve two optimization programs onto feasible set. The main idea of the proposed algorithms is that at every iterative step, we have replaced the second optimization program by that one on a specific half-space which can be performed more easily. The weakly and strongly convergent theorems are established under widely used assumptions for bifunctions.

Extragradient subgradient methods for solving bilevel equilibrium problems

“…In 2008, Tran et al [25] proposed the extragradient algorithm for solving the equilibrium problem by using the strongly convex minimization problem to solve at each iteration. Furthermore, Hieu [9] introduced subgradient extragradient methods for pseudomonotone equilibrium problem and the other methods (see the details in [1, 8, 10, 15, 17, 22, 28]).…”