集优化问题的适定性和稳定性  

Well-posedness and stability of set optimization problems

作　　者：孟旭东[1] MENG Xudong(Science College of Nanchang Hangkong University,Gongqingcheng 332020,Jiangxi,China)

机构地区：[1]南昌航空大学科技学院,江西共青城332020

出　　处：《云南大学学报（自然科学版）》2024年第5期801-810,共10页Journal of Yunnan University(Natural Sciences Edition)

基　　金：江西省教育厅科学技术重点项目(GJJ181565,GJJ191614,GJJ218701);南昌航空大学校级重点科学技术项目(KYKJ2108);南昌航空大学校级自然科学基金(KYZK2301).

摘　　要：在赋范线性空间中讨论了集优化问题的适定性和稳定性.首先,给出集优化问题3种适定性的概念及其关系.其次,借助局部锥Lipschitz连续性并运用分析方法刻画了集优化问题的适定性.最后,研究了具锥Lipschitz连续性集值映射的参数集优化问题的Berge连续性和极小解映射的紧性.The well-posedness and stability of set optimization problems are discussed in the normed vector space.Firstly,The concepts for three kinds of well-posedness to set optimization problems and their relations are given.Secondly,under the local cone Lipschitz continuity the well-posedness of set optimization problems is characterized by using the analytical method.Finally,the Berge semi-continuity and compactness of minimal solution mappings are studied for parametric set optimization involving the cone Lipschitz continuous set-valued mapping.

关 键 词：集优化问题 适定性 稳定性 锥Lipschitz连续性 

分 类 号：O221.3[理学—运筹学与控制论]