约束集值优化问题Henig有效解的最优性条件  

Optimality conditions for Henig efficient solutions of constrained set-valued optimization problems

作　　者：孟旭东[1] 郭林[1] MENG Xudong;GUO Lin(Science College,Nanchang Hangkong University,Gongqingcheng 332020,China)

机构地区：[1]南昌航空大学科技学院,江西共青城332020

出　　处：《安徽大学学报（自然科学版）》2023年第2期31-36,共6页Journal of Anhui University(Natural Science Edition)

基　　金：江西省教育厅科学技术重点研究项目(GJJ181565,GJJ191614,GJJ218701);南昌航空大学科技学院重点科学技术研究项目(KYKJ2108)。

摘　　要：在实赋范线性空间中研究了约束集值优化问题Henig有效解的最优性条件.首先,引进了集值映射的Henig有效解次微分的概念.其次,给出了锥-凸集值映射的支撑函数和Henig有效解次微分的性质.最后,运用分析方法,借助凸集分离定理建立了约束集值优化问题Henig有效解最优性定理.In this paper,the optimality conditions for Henig efficient solutions of constrained set-valued optimization problems in real normed linear spaces were studied.Firstly,the concept of Henig efficient solution subdifferential of set-valued mapping was introduced.Secondly,the support functions of cone convex set-valued maps and the properties of Henig efficient solutions were given.Finally,by using the analytic method and the separation theorem of convex sets,the optimality theorem of Henig efficient solution for constrained set-valued optimization problems was established.

关 键 词：集值映射 HENIG有效解 次微分 支撑函数 

分 类 号：O221.3[理学—运筹学与控制论]