A dual view of equilibrium problems

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.