集值优化问题的最优性条件：基于广义C-子凸和伪相对内部的择一性定理的一个应用

摘要

该文首先通过伪相对内部的概念定义了广义 C -子凸集值映射。其次刻画了一些伪相对内部的性质，然后利用广义 C -子凸和伪相对内部的分离定理，建立了择一性定理。最后利用所得到的择一性定理，建立了一些有关广义 C -子凸集值最优化问题的最优性条件。本文对参考文献中的一些结论进行了推广和改进。%In this paper,a new generalized sub - convex set - valued map based on the pseudo - relative in-terior was introduced,and some useful properties on pseudo - relative interior were given. Then,an alternative theorem based on generalized C - sub - convexity and a separation theorem involving the pseudo - relative interior were obtained. As an application,some optimality conditions of set - valued optimization problems by an alterna-tive theorem were put forward. And some results in the literature were also generalized and improved in this pa-per.