Geodesic
Gerstewitz nonlinear scalar functional and the applications in vector optimization problems
Filomat, Tome 36 (2022) no. 16, p. 5615

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

In this paper, we study the properties of Gerstewitz nonlinear scalar functional with respect to co-radiant 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.
DOI : 10.2298/FIL2216615G
Classification : 90C29, 90C30
Keywords: Gerstewitz nonlinear scalar functional, Co-radiant function, Radiant function, Vector optimization problem, Approximate solutions, Lagrange conditions 
Ying Gao; Liping Tang. Gerstewitz nonlinear scalar functional and the applications in vector optimization problems. Filomat, Tome 36 (2022) no. 16, p. 5615 . doi: 10.2298/FIL2216615G
@article{10_2298_FIL2216615G,
     author = {Ying Gao and Liping Tang},
     title = {Gerstewitz nonlinear scalar functional and the applications in vector optimization problems},
     journal = {Filomat},
     pages = {5615 },
     year = {2022},
     volume = {36},
     number = {16},
     doi = {10.2298/FIL2216615G},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2216615G/}
}
TY  - JOUR
AU  - Ying Gao
AU  - Liping Tang
TI  - Gerstewitz nonlinear scalar functional and the applications in vector optimization problems
JO  - Filomat
PY  - 2022
SP  - 5615 
VL  - 36
IS  - 16
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2216615G/
DO  - 10.2298/FIL2216615G
LA  - en
ID  - 10_2298_FIL2216615G
ER  - 
%0 Journal Article
%A Ying Gao
%A Liping Tang
%T Gerstewitz nonlinear scalar functional and the applications in vector optimization problems
%J Filomat
%D 2022
%P 5615 
%V 36
%N 16
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2216615G/
%R 10.2298/FIL2216615G
%G en
%F 10_2298_FIL2216615G

Cité par Sources :