Details
| Original language | English |
|---|---|
| Pages (from-to) | 2653-2665 |
| Number of pages | 13 |
| Journal | Journal of Nonlinear and Convex Analysis |
| Volume | 20 |
| Issue number | 12 |
| Publication status | Published - 2019 |
| Externally published | Yes |
Abstract
The aim of this paper is to present new characterizations of explic¬itly cone-quasiconvex vector functions with respect to a polyhedral cone of a finite-dimensional Euclidean space. These characterizations are given in terms of classical explicit quasiconvexity of certain real-valued functions, defined by composing the vector-valued function with appropriate scalarization functions, namely the extreme directions of the polar cone or some nonlinear scalarization functions, currently used in vector optimization.
Keywords
- Extreme direc¬tions, Generalized convex vector functions, Nonlinear scalarization function, Polyhedral cones
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
- Mathematics(all)
- Geometry and Topology
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In: Journal of Nonlinear and Convex Analysis, Vol. 20, No. 12, 2019, p. 2653-2665.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Characterizations of explicitly quasiconvex vector functions w.r.t. polyhedral cones
AU - Günther, Christian
AU - Popovici, Nicolae
N1 - Publisher Copyright: © 2019 Yokohama Publications. All rights reserved.
PY - 2019
Y1 - 2019
N2 - The aim of this paper is to present new characterizations of explic¬itly cone-quasiconvex vector functions with respect to a polyhedral cone of a finite-dimensional Euclidean space. These characterizations are given in terms of classical explicit quasiconvexity of certain real-valued functions, defined by composing the vector-valued function with appropriate scalarization functions, namely the extreme directions of the polar cone or some nonlinear scalarization functions, currently used in vector optimization.
AB - The aim of this paper is to present new characterizations of explic¬itly cone-quasiconvex vector functions with respect to a polyhedral cone of a finite-dimensional Euclidean space. These characterizations are given in terms of classical explicit quasiconvexity of certain real-valued functions, defined by composing the vector-valued function with appropriate scalarization functions, namely the extreme directions of the polar cone or some nonlinear scalarization functions, currently used in vector optimization.
KW - Extreme direc¬tions
KW - Generalized convex vector functions
KW - Nonlinear scalarization function
KW - Polyhedral cones
UR - http://www.scopus.com/inward/record.url?scp=85090791484&partnerID=8YFLogxK
M3 - Article
VL - 20
SP - 2653
EP - 2665
JO - Journal of Nonlinear and Convex Analysis
JF - Journal of Nonlinear and Convex Analysis
SN - 1345-4773
IS - 12
ER -