Existence and convergence of optimal points with respect to improvement sets

In this paper new results concerning the existence and stability of optimal points in the context of optimization problems in infinite dimensional spaces are presented. Such optimality is defined through the generalized criteria of improvement sets. These results enhance those reported in a previous paper about the same argument and include a theorem which improves the Bishop-Phelps principle about the domination property. Most are an enhancement also in the case in which the improvement set is reduced to a cone. Moreover, a new definition of minimal points with respect to the interior of the feasible set is introduced and used in the study of stability.