A Kind of Equivalence of Three Nonlinear Scalarization Functions in Vector Optimization  

作　　者：LI Fei YANG Xinmin 

机构地区：[1]School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China [2]School of Mathematical Sciences,Chongqing Normal University,Chongqing 400047,China

出　　处：《Journal of Systems Science & Complexity》2021年第2期692-705,共14页系统科学与复杂性学报（英文版）

基　　金：the National Natural Science Foundation of China under Grant Nos.11601248,11431004,11971084。

摘　　要：In this paper,by the notions of base functionals and augmented dual cones,the authors indicate firstly that the norms,Gerstewitz functionals and oriented distance functions have common characteristics with base functionals.After that,the equivalence of these three sublinear functions on the ordering cone is established by using the structures of augmented dual cones under the assumption that it has a bounded base.However,the authors show that two superlinear functions do not have similar relations with the norms ahead.More generally,the equivalence of three sublinear functions outside the negative cone has also been obtained in the end.

关 键 词：Base functionals Gerstewitz functionals norms oriented distance functions vector optimization 

分 类 号：O221.2[理学—运筹学与控制论]