A dual view of equilibrium problems

Abstract

The aim of this paper is to introduce and study a dual problem associated to a generalized equilibrium problem ( GEP ) . We show that the solutions of ( GEP ) and its dual are strictly related to the saddle points of an associated Lagrangian function, and, under some suitable conditions, to the solutions of a family of parametric optimization problems and their dual problems. Our results allow us to show that well-known concepts and results from duality theory of some important particular cases of ( GEP ) like variational inequalities and optimization problems can be recovered.