Gerstewitz nonlinear scalar functional and the applications in vector optimization problems-Reference-Cited by-同舟云学术

Gerstewitz nonlinear scalar functional and the applications in vector optimization problems

Published:2022 Issue:16 Volume:36 Page:5615-5629
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Gao Ying¹,Tang Liping²

Affiliation:

1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, China

2. National Center for Applied Mathematics in Chongqing, Chongqing Normal University, Chongqing, China

Abstract

In this paper, we study the properties of Gerstewitz nonlinear scalar functional with respect to coradiant set and radiant set in real linear space. With the help of nonconvex separation theorem with respect to co-radiant set, we first obtain that Gerstewitz nonlinear scalar functional is a special co-radiant(radiant) functional when the corresponding set is a co-radiant(radiant) set. Based on the subadditivity property of this functional with respect to the convex co-radiant set, we calculate its Fenchel(approximate) subdifferential. As the applications, we derive the optimality conditions for the approximate solutions with respect to co-radiant set of vector optimization problem. We also state that this special functional can be used as a coherent measure in the portfolio problem.

Publisher

National Library of Serbia

Subject

General Mathematics

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