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运筹学学报 ›› 2015, Vol. 19 ›› Issue (4): 107-113.doi: 10.15960/j.cnki.issn.1007-6093.2015.04.010

• 运筹学 • 上一篇    下一篇

向量优化中Free Disposal集的某些对偶性质

唐莉萍1,*, 杨玉红2,3   

  1. 1.重庆工商大学数学与统计学院, 重庆 400067;2. 内蒙古大学数学科学学院,呼和浩特 010021; 3.长江师范学院数学与统计学院, 重庆 408100
  • 收稿日期:2014-10-24 出版日期:2015-12-15 发布日期:2015-12-15
  • 通讯作者: 唐莉萍 tanglipings@163.com
  • 基金资助:

    1.国家自然科学基金重点项目(No.11431004);2.国家自然科学基金(No.11271391);

    3.国家自然科学基金青年科学基金项目(Nos.11201511,11301571);4.重庆市科委项目(cstc2014pt-sy00001)

Some dual characterizations of free disposal sets in vector optimization

TANG Liping1,*,  YANG Yuhong2,3   

  1. 1.College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China; 2.College of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China; 3.School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100, China
  • Received:2014-10-24 Online:2015-12-15 Published:2015-12-15

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摘要：

在分离局部凸空间中考虑free disposal集的对偶性质, 其中free disposal集是 指与凸锥的代数和仍是其本身的集合.在E_1或E_2是free disposal集的条件下,证明了(E_1\cap E_2)^+=E_1^++ E_2^+和E_1^+ \cap E_2^+=(E_1+E_2)^+等对偶结果.

关键词: 向量优化, free disposal集, 对偶集

Abstract:

In this paper, we focus on some dual characterizations of free disposal sets in a separated locally convex space, in which, free disposal set means that its algebraic sum with a convex cone is still itself. Under the assumption that E_1 or E_2 is free disposal set, we proved some dual results, such as (E_1\cap E_2)^+=E_1^++ E_2^+, E_1^+ \capE_2^+=(E_1+ E_2)^+, etc.

Key words: vector optimization, free disposal set, dual set