Details
| Original language | English |
|---|---|
| Pages (from-to) | 325-333 |
| Number of pages | 9 |
| Journal | Journal of Applied and Numerical Optimization |
| Volume | 1 |
| Issue number | 3 |
| Early online date | 31 Dec 2019 |
| Publication status | Published - 2019 |
| Externally published | Yes |
Abstract
The aim of this paper is to present new characterizations of cone-convex and explicitly cone-quasiconvex vector functions with respect to a proper closed solid convex cone of a real linear topological space. These characterizations are given in terms of classical convexity and explicit quasiconvexity of certain real-valued functions, defined by means of the nonlinear scalarization function introduced by Gerstewitz (Tammer) in 1983.
Keywords
- Cone-convexity, Cone-quasiconvexity, Explicit cone-quasiconvexity, Linear perturbation, Nonlinear scalarization
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
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In: Journal of Applied and Numerical Optimization, Vol. 1, No. 3, 2019, p. 325-333.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - The role of nonlinear scalarization functions in characterizing generalized convex vector functions
AU - Günther, Christian
AU - Popovici, Nicolae
N1 - Publisher Copyright: © 2019 Journal of Applied and Numerical Optimization.
PY - 2019
Y1 - 2019
N2 - The aim of this paper is to present new characterizations of cone-convex and explicitly cone-quasiconvex vector functions with respect to a proper closed solid convex cone of a real linear topological space. These characterizations are given in terms of classical convexity and explicit quasiconvexity of certain real-valued functions, defined by means of the nonlinear scalarization function introduced by Gerstewitz (Tammer) in 1983.
AB - The aim of this paper is to present new characterizations of cone-convex and explicitly cone-quasiconvex vector functions with respect to a proper closed solid convex cone of a real linear topological space. These characterizations are given in terms of classical convexity and explicit quasiconvexity of certain real-valued functions, defined by means of the nonlinear scalarization function introduced by Gerstewitz (Tammer) in 1983.
KW - Cone-convexity
KW - Cone-quasiconvexity
KW - Explicit cone-quasiconvexity
KW - Linear perturbation
KW - Nonlinear scalarization
UR - http://www.scopus.com/inward/record.url?scp=85104528311&partnerID=8YFLogxK
U2 - 10.23952/jano.1.2019.3.09
DO - 10.23952/jano.1.2019.3.09
M3 - Article
VL - 1
SP - 325
EP - 333
JO - Journal of Applied and Numerical Optimization
JF - Journal of Applied and Numerical Optimization
SN - 2562-5527
IS - 3
ER -