集值映射最优化问题的严有效解集的连通性及应用  

CONNECTEDNESS OF THE STRICTLY EFFICIENT SOLUTION SETS OF THE OPTIMIZATION PROBLEM FOR A SET VALUED MAPPING AND APPLICATIONS

作　　者：仇秋生[1] 

机构地区：[1]五邑大学数学物理系

出　　处：《高校应用数学学报（A辑）》1999年第1期85-92,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

摘　　要：本文对集值映射最优化问题引入严有效解的概念．证明了当目标函数为锥类凸的集值映射时，其目标空间里的严有效点集是连通的；若目标函数为锥凸的集值映射时，其严有效解集也是连通的．作为应用，讨论了超有效解集的连通性．In this paper,a concept of strictly efficient solution of the optimization problem for a set valued mapping is introduced.It is proved that strictly efficient point set of the objective space is connected when objective function is cone convex like,and that if objective function is cone convex set valued mapping,then strictly efficient solution set is also connected.As an interesting application of the results in this paper,the connectedness of super efficient solution sets is discussed.

关 键 词：集值映射 严有效点 严有效解 连通性 最佳化 

分 类 号：O224[理学—运筹学与控制论]