集值映射的一种锥凸性及标量化  

A kind of cone-convexity for set-valued maps and its scalarization

作　　者：李飞[1] 唐莉萍[2] 杨新民[3] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]重庆工商大学数学与统计学院,重庆400067 [3]重庆师范大学数学科学学院,重庆400047

出　　处：《运筹学学报》2016年第4期21-29,共9页Operations Research Transactions

基　　金：国家自然科学基金重点项目(Nos.11431004;11271391;11601248);重庆市科委项目(No.cstc2014pt-sy00001)

摘　　要：在一种集合偏序关系下提出了集值映射的标量锥拟凸概念,讨论了它与各种锥凸性的关系.然后对恰当锥拟凸性得到了某种水平集意义下的刻画.同时建立了集值映射的各种锥凸性通过实值单调增加凸函数表示的标量化复合法则.最后给出了利用Gerstewitz泛函表示的对集值映射的锥拟凸性的标量化刻画.In this paper, we firstly introduce the notion of scalar cone-quasiconvexity for set-valued maps and discuss the relationships among several cone-convexities. A char- acterization for proper cone-quasiconvexity of set-valued maps is also given in the sense of a type of level set. Meanwhile, the composition rule of cone-convexity of set-valued maps is established by scalar increasing convex functions. We obtain a characterization for cone-quasiconvexity of set-valued maps by Gerstewitz functional finally.

关 键 词：集值映射 锥凸性 Gerstewitz泛函 标量化 

分 类 号：O221.6[理学—运筹学与控制论]