Operations Research Transactions ›› 2015, Vol. 19 ›› Issue (4): 107-113.doi: 10.15960/j.cnki.issn.1007-6093.2015.04.010

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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

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