多目标最优化恰当有效解的稳定性  

Stability of proper efficient solution for multi-objective optimization

作　　者：何莉敏[1] 李德荣[1] 侯玉双[1] 王娟[1] 李玉[1] 

机构地区：[1]内蒙古科技大学数理与生物工程学院应用数学系,内蒙古包头014010

出　　处：《纯粹数学与应用数学》2011年第1期32-36,共5页Pure and Applied Mathematics

基　　金：内蒙古教育厅高等学校科研项目(NJzy08075);内蒙古科技大学教学研究重点项目(JY2009017)

摘　　要：主要研究当两种类型的参数扰动时,多目标最优化问题中恰当有效解的稳定性.在点集映射的连续性意义下,分析讨论这种稳定性问题并分别给出引起扰动的两参数u,v所对应的点集映射Q1(u)和Q2(v),同时严格证明了在两个闭凸锥U,V上Q1(u)和Q2(v)的连续性定理.最后,通过附注对其进行补充和改进.This paper, the stability of the set of proper efficient solutions is studied with respect to two types of perturbation in multi-objective optimization problem. At the point-to-set mapping of the sense of continuity, the stability is analyzed and discussed, and two point-to-set mappings Q1（u） and Q2（v） with respectto u,v, respectively, are given. At the same time,the theorems of continuity of Q1（u） and Q2（v） are provedstrictly on condition that the domination structure are assumed to be two closed convex cones. Finally, some supplements and improvements are made by remarks.

关 键 词：多目标最优化 点集映射 上半连续 下半连续 恰当有效解 

分 类 号：O221.6[理学—运筹学与控制论]