Computational Errors of the Extragradient Method for Equilibrium Problems

Our aim in this paper is to study variants and computational errors of the extragradient method for solving equilibrium problems. First, we consider convergence of the method when domains in the auxiliary subproblems of the extragradient algorithm are replaced by outer and inner approximation polyhedra. Then, computational errors are showed under the asymptotic optimality condition, but the bifunction must satisfy certain Lipschitz-type continuous conditions. Next, by using Armijo-type linesearch techniques commonly used in variational inequalities, we obtain an approximation linesearch algorithm without Lipschitz continuity. Convergence analysis of the algorithms is considered under mild conditions on the iterative parameters.