关于超有效点的注记  

Notes on Super Efficient Points

作　　者：刘涌泉[1] 

机构地区：[1]深圳广播电视大学

出　　处：《应用数学》1999年第3期128-132,共5页Mathematica Applicata

摘　　要：本文首先给出了赋范空间中Ｂｏｒｗｅｉｎ超有效点定义的二个与范数无关的等价形式，从而得出推广超有效点到局部凸空间的二个途径，并通过例子说明其中之一是不恰当的．我们还给出了超有效点集连通的二个结果．最后，我们指出文［１］引入的严有效点就是Ｈｅｎｉｇ有效点，其主要定理（［１］定理７）是［２］中定理３．We first give the two equivalent forms of the definition of a Borweins super efficient point in a normal space,which are not related to the norm.In view of this fact,we obtain two ways by which the concept of a super efficient point can be generalized to a locally convex space in from and considered the suitability of the two ways.We also establish the connectedness results of a super efficient point set.Moreover,We point out that the main concept of a strictly efficient point is equal to the concept of a Henig efficient point and that the main theorem in is constained in theorem 3.3 in .

关 键 词：超有效点 局部凸空间 连通性 向量优化 赋范空间 

分 类 号：O224[理学—运筹学与控制论]