基于改进集的参数集值优化问题解集映射的稳定性  

Stability of solution set mapping for parametric set-valued optimization problems via improved sets

作　　者：孟旭东[1] MENG Xudong(Science and Technology College of NCHU,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：《中山大学学报（自然科学版）（中英文）》2022年第2期180-188,共9页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金(11201216);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,GJJ181567);校级重点科学技术研究项目(KJKT2108)。

摘　　要：在实赋范线性空间中讨论了基于改进集的参数集值优化问题解集映射的稳定性。在目标函数具有CHausdorff连续性和E-闭性及可行集具有连续性和紧凸性条件下,分析了关于改进集E的水平集值映射的上半连续性和下半连续性。在此基础上,在目标函数构成的序偶映射具有严格E-拟凸性基本假设下,通过分析的方法获得了具改进集的参数集值优化问题解集映射的Berge连续性、Hausdorff连续性、C-Hausdorff连续性和紧闭性定理。The stability of solution set mapping for parameter set-valued optimization problems via im‐proved sets in real normed vector space is discussed.The upper semi-continuity and lower semi-conti‐nuity of level set-valued mappings via improved sets E is analyzed under the conditions that the objec‐tive function having C-Hausdorff continuity and E-closure and the feasible set having continuity and compact convexity.On this basis,through the method of analysis,the theorems of the Berge continu‐ity,Hausdorff continuity,C-Hausdorff continuity compactness and closeness of solution set mapping for parametric set-valued optimization problems via improved sets are obtained by the method of analy‐sis with the help of the basic assumption of strict-quasi-convexity for the ordered-even mappings com‐posed of objective functions.

关 键 词：解集映射 改进集 稳定性 连续性 参数集值优化问题 

分 类 号：O221.3[理学—运筹学与控制论]