Existence and Convergence of Optimal Points with Respect to Improvement Sets
研究了无限维空间中基于改进集准则的最优点的存在性与稳定性，改进了Bishop-Phelps支配性质定理，并引入可行集内部极小点的新定义用于稳定性分析。
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.