向量优化中有效点的存在性  

Existence of Efficient Points in Vector Optimization

作　　者：张燕[1] 杨吉[2] 

机构地区：[1]云南大学数学系,云南昆明650091 [2]空军长春飞行学院,吉林长春130000

出　　处：《应用泛函分析学报》2002年第1期55-59,共5页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金项目 (1 9861 0 0 4)

摘　　要：分别在有 pre-order的无线性结构的集合和拓扑空间中 ,给出了有效点的存在性 .作为应用 ,讨论了向量优化问题中解的存在性 .最后给出了紧、弱紧、锥紧、锥半紧、上序紧、下序紧、上序半紧、准上序半紧和准下序半紧等之间的关系 .In this paper, we give a general existence result of efficient points in a set without linear structure equipped with a pre\|order. In a topological space equipped with a pre\|order, we prove existence result of efficient points. As applications, we study the solution problem in vector optimization. At last, we give the relations among compactness, weakly compactness, cone compactness, cone semi\|compactness, upper order compactness, lower order compactness, upper order semi\|compactness, lower order semi\|compactness, quasi\|upper order semi\|compactness, quasi\|lower order semi\|compactness.

关 键 词：向量优化 有效点 pre-order 上序紧 下序紧 上序半紧 下序半紧 准上序半紧 准下序半紧 

分 类 号：O177[理学—数学]