集合最优化中几类最优集的性质  

On the Properties of Several Types of Optimal Sets in Set-Optimization

作　　者：李毛亲[1] 冯国[1] 

机构地区：[1]台州学院数学系,浙江临海317000

出　　处：《中北大学学报（自然科学版）》2012年第5期499-502,共4页Journal of North University of China(Natural Science Edition)

基　　金：浙江省台州学院重点科研项目(08ZD03)

摘　　要：在偏序拓扑线性空间中介绍了集合之间的下关系以及与此相关的集合最优化问题及其最优集的概念.探讨了该集合最优化问题的最优集的基本性质,得到了某些相关集簇的最优集之间的关系以及一个集簇的最优集与其子集簇的最优集之间的关系.研究了控制结构的变化对一个集簇的最优集的影响,得到了当控制结构扩大时一个集簇在不同的控制结构下其最优集之间的关系,并把该结论与向量最优化的相应结论进行了比较.A set relation,called lower relation,and set optimization problem and the optimal set,corresponding to the lower relation,are introduced in a partially topological linear space.Some basic properties of the optimal set are concerned.The relationship between the optimal sets of different families are investigated.The relationship between the optimal sets of a family and its subfamily are developed.Also the pertinence of the optimal sets for a family and the domination constructions is studied.The relations between the optimal sets of a family under the different domination constructions are given.A comparation is made between the conclusions in the set optimization and that in the vector optimization.

关 键 词：集合最优化 下关系 上关系 l-最优集 弱l-最优集 绝对l-最优集 

分 类 号：O224[理学—运筹学与控制论]