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

Abstract

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.