向量优化问题局部近似解的等价性  

Equivalence of Local Approximate Solutions for Vector Optimization Problems

作　　者：孔翔宇 KONG Xiang-yu(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,China)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021

出　　处：《数学的实践与认识》2020年第9期194-200,共7页Mathematics in Practice and Theory

基　　金：宁夏高等学校科学研究项目(NGY2017158)。

摘　　要：主要研究两种不同序关系下向量优化问题的近似解.一种是正锥序关系下的近似解,另一种是多面体锥序关系下的近似解.针对这两种序关系下向量优化问题的近似解,建立了局部近似最优解和μ阶严格局部近似最优解之间的等价关系,同时构建了这两种序关系下近似有效点集之间的等价关系.In this paper we consider approximate solutions by two different kinds of order relations for vector optimization problems.One is the approximate solution of order relations introduced by a positive cone,the other one is the approximate solution of order relations introduced by a pointed polyhedral cone.For the approximate solutions under above two kinds of order relations,the equivalent relations between local approximate optimal solutions and strict local approximate optimal solutions of order μ are established.Moreover,the equivalence relations between approximate efficient point sets under two kinds of order relations are constructed.

关 键 词：向量优化问题 局部近似最优解 μ阶严格局部近似最优解 多面体锥 正锥 

分 类 号：O224[理学—运筹学与控制论]