集值映射最优化问题超有效解集的连通性  

THE CONNECTEDNESS OF THE SUPER EFFICIENT SOLUTION SETS OF THE OPTIMIZATION PROBLEM FOR A SET-VALUED MAPPING

作　　者：仇秋生[1] 傅万涛[2] 

机构地区：[1]五邑大学数学物理系,广东江门529020 [2]南昌大学数学系,南昌330047

出　　处：《系统科学与数学》2002年第1期107-114,共8页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金资助课题

摘　　要：本文在局部凸空间中对集值映射最优化问题引入超有效解的概念．首先研究了超 有效点的一些重要特性．其后证明了当目标函数为锥类凸的集值映射时，其目标空间里 的超有效点集是连通的；若目标函数为锥凸的集值映射时，其超有效解集也是连通的．In this paper, we introduce a concept of super efficient solution of the opti-mization problem for a set-valued mapping. Firstly, we discuss some characterizations of super efficient point of the vector optimization. Secondly, we prove that the super efficient point set of the objective space is connected when the objective function is cone convex-like, and obtain that if the objective function is a cone convex set-valued mapping, then the super efficient solution set is also connected.

关 键 词：集值映射 超有效解 连通性 基底 最优化问题 

分 类 号：O224[理学—运筹学与控制论]