含参集值优化问题近似解集的稳定性  

Stability of approximate solutions set for parametric set-valued optimization problem

作　　者：孟旭东[1] MENG Xu-dong(Science and Technology 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）》2022年第4期663-674,共12页Journal of Yunnan University(Natural Sciences Edition)

基　　金：江西省教育厅科学技术重点研究项目(GJJ181565,GJJ191614,GJJ218701);江西省教育厅科学技术研究项目(GJJ161597);南昌航空大学校级重点科学技术研究项目(KJKT2108)。

摘　　要：在赋范线性空间中讨论了含参集值优化问题近似解集的稳定性.首先,给出了含参集值优化问题2类(弱)近似解的概念及其性质关系.其次,在目标函数集值映射具严格近似上(下)锥凸性假设下,获得了含参集值优化问题2类(弱)近似解集的上半连续性定理.最后,结合水平映射的方法研究了含参集值优化问题2类(弱)近似解集的下半连续最优性充分条件.The stability of approximate solutions set to parametric set-valued optimization problem is discussed in normed linear space.Firstly,the concepts and properties for two kinds of(weak)approximate solutions to parametric set-valued optimization problem are given.Secondly,under the assumption that the setvalued mapping of objective function having strict approximate upper(lower)cone convexity,the upper semicontinuity theorems for two kinds of(weak)approximate solutions set to parametric set-valued optimization problems are obtained.Finally,the sufficient conditions for the lower semicontinuity of two kinds of(weak)approximate solution sets to parametric set-valued optimization problems are studied by using the method of level mapping.

关 键 词：含参集值优化问题 集值映射 近似解 上半连续性 下半连续性 

分 类 号：O221.3[理学—运筹学与控制论]