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

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.