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  

Application of Alternative Theorems on Generalized C-Sub-convexity and Pseudo-Relative Interior

作　　者：邓雪彬 

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《绵阳师范学院学报》2015年第5期19-25,47,共8页Journal of Mianyang Teachers＇ College

基　　金：国家自然科学基金(11371015);教育部科学技术重点项目(211163);四川省青年科技基金(2012JQ0035)

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.

关 键 词：伪相对内部 广义C-子凸集值映射 分离定理 最优性条件 

分 类 号：O224[理学—运筹学与控制论]