上图像拓扑下向量优化问题弱有效解的通有稳定性  

Generic Stability of the Weakly Efficient Solutions in Vector Optimization Problems in Epigraph Topology Case

作　　者：彭定涛[1] 叶明武[1] 刘开拓[1] 

机构地区：[1]贵州大学应用数学所,贵州贵阳550003

出　　处：《贵州工业大学学报（自然科学版）》2005年第1期1-5,13,共6页Journal of Guizhou University of Technology(Natural Science Edition)

基　　金：贵州省自然科学基金资助项目(黔基合计字20023107)

摘　　要：用函数的上图象之间的Hausdorff距离定义向量值函数间的距离,在此弱拓扑下研究了定义在紧距离空间上的一类具有普遍意义的n维向量值函数弱有效解的稳定性,指出在Baire分类意义下,大多数这类向量值函数的弱有效解是稳定的,且任一n维向量值函数都可以用所谓的本质函数来逼近。The distance between two functionals is defined by the Hausdorff distance between the epigraphs of the two functionals. In this weak topology case, we research the stability of the weakly efficient solutions of a kind of general meanings n-dimensioned vector-valued functionals. As results, we point out that, from the viewpoint of Baire's category, most of the vector optimization problems have stable weakly efficient solutions and that any this kind of function can be arbitrarily approximated by a sequence of so-called essential vector-valued functionals.

关 键 词：弱有效解 usco映射 通有的 本质的 稳定性 

分 类 号：O225[理学—运筹学与控制论]