关于多目标最优化问题的有效点

ON EFFICIENT POINTS IN MULTI-OBJECTIVE OPTIMIZATION PROBLEMS

本文证明了:在有序局部凸线性拓扑空间中,一个集合的有效点必为该集合的边界点或孤立点.本文还分别给出了使一点为一个集合的有效点、严格有效点和弱有效点的充分必要条件.此外,还证明了:在有序可分线性赋范空间中,每个非空弱紧集至少具一个有效点.

In this paper,it is proved that an efficient point of a set inan ordered locally convex linear topological space must be the boundary pointor isolated point of the set.The sufficient and necessary conditions fora point of a set to be efficient,strictly efficient or weakly efficient arerespectively given.Also,it is shown that any nonempty weakly compact setin an ordered separable normed space has at least an efficient point.