Operations Research Transactions ›› 2021, Vol. 25 ›› Issue (2): 135-143.doi: 10.15960/j.cnki.issn.1007-6093.2021.02.011

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The equivalent representation of co-radiant sets and its application in multi-objective optimization problems

Wenyi WANG1, Ying GAO1, Fuping LIU1,*()   

  1. 1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
  • Received:2020-07-03 Online:2021-06-15 Published:2021-05-06
  • Contact: Fuping LIU E-mail:lfp751214@163.com

Abstract:

As a special abstract convex (concave) sets, radiant sets and co-radiant sets play the important roles in abstract convex analysis and the theory of multiobjective optimization problems. We first establish the equivalent characterizations for the radiant sets and co-radiant sets. Finally, we apply important properties to the characterization of the approximate solutions of the vector optimization problems, and obtain the equivalent characterization of the approximate solution sets.

Key words: co-radiant sets, radiant sets, equivalent representations, vector optimization problems, approximate solutions

CLC Number: