Well-posedness for equilibrium problems and for optimization problems with equilibrium constraints

In this paper we generalize the concepts of well-posedness to equilibrium problems and to optimization problems with equilibrium constraints. We establish some metric characterizations of well-posedness for equilibrium problems and for optimization problems with equilibrium constraints. We prove that under suitable conditions, the well-posedness is equivalent to the existence and uniqueness of solutions. The corresponding concepts of well-posedness in the generalized sense are also introduced and investigated for equilibrium problems and for optimization problems with equilibrium constraints.