集优化问题的适定性和稳定性

Well-posedness and stability of set optimization problems

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.