集值映射的一种锥凸性及标量化

doi:10.15960/j.cnki.issn.1007-6093.2015.04.003

运筹学学报

集值映射的一种锥凸性及标量化

李飞^1,* 唐莉萍²杨新民³

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

收稿日期:2015-11-12 出版日期:2016-12-15 发布日期:2016-12-15
通讯作者: 李飞 lifeimath@163.com
基金资助:
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)

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

LI Fei^1,* TANG Liping² YANG Xinmin³

1. School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; 2. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China; 3. School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, China

Received:2015-11-12 Online:2016-12-15 Published:2016-12-15

摘要/Abstract

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.

关键词: 集值映射, 锥凸性, Gerstewitz泛函, 标量化

Abstract:

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 characterization 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.

Key words: set-valued maps, cone-convexity, Gerstewitz functional, scalarizations

李飞, 唐莉萍, 杨新民. 集值映射的一种锥凸性及标量化[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2015.04.003.

LI Fei, TANG Liping, YANG Xinmin. A kind of cone-convexity for set-valued maps and its scalarization[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2015.04.003.

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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

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