SOME ITERATIVE METHODS FOR QUASI-EQUILIBRIUM PROBLEMS

Abstract

In this paper we present two new extensions of Korpelevich's extragraclient method for solving the scalar Quasi-Equilibrium Problem (QEP) in Euclidean space. In both extensions we replace the second orthogonal projection in the correction step of the extragradient method by an Armijo linesearch adapted to (QEP). We show that in both extensions we obtain, under mild conditions and without a Lipschitz condition, the global convergence of our iterative methods for computing a quasi-equilibrium solution.