Details
| Original language | English |
|---|---|
| Journal | OPTIMIZATION |
| Early online date | 1 Aug 2024 |
| Publication status | E-pub ahead of print - 1 Aug 2024 |
Abstract
We establish a new concept of semistrict quasiconvexity for vector functions defined on a nonempty convex set in a real linear space X that take values in some real topological linear space Y, partially ordered by a proper solid convex cone C. The so-called semistrict C-quasiconvexity notion recovers the classical concept of semistrict quasiconvexity of scalar functions when (Formula presented.) and (Formula presented.). Additionally, analogous to the scalar scenario, if the cone C is closed, a vector function is both semistrictly C-quasiconvex and C-quasiconvex (in the sense of Luc, 1989) if and only if it is explicitly C-quasiconvex (in the sense of Popovici, 2007). Finally, we convey a characterization of semistrictly C-quasiconvex functions by means of scalar semistrictly quasiconvex functions that are compositions of the nonlinear scalarization functions introduced by Gerstewitz (Tammer) in 1983 with the initial vector function. In light of this characterization, the new concept of semistrict C-quasiconvexity seems to be a natural vector counterpart for the scalar concept of semistrict quasiconvexity.
Keywords
- Generalized convexity, nonlinear scalarization function, vector function
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Applied Mathematics
- Decision Sciences(all)
- Management Science and Operations Research
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In: OPTIMIZATION, 01.08.2024.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A new concept of semistrict quasiconvexity for vector functions
AU - Günther, Christian
AU - Orzan, Alexandru
AU - Popovici, Nicolae
N1 - Publisher Copyright: © 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
PY - 2024/8/1
Y1 - 2024/8/1
N2 - We establish a new concept of semistrict quasiconvexity for vector functions defined on a nonempty convex set in a real linear space X that take values in some real topological linear space Y, partially ordered by a proper solid convex cone C. The so-called semistrict C-quasiconvexity notion recovers the classical concept of semistrict quasiconvexity of scalar functions when (Formula presented.) and (Formula presented.). Additionally, analogous to the scalar scenario, if the cone C is closed, a vector function is both semistrictly C-quasiconvex and C-quasiconvex (in the sense of Luc, 1989) if and only if it is explicitly C-quasiconvex (in the sense of Popovici, 2007). Finally, we convey a characterization of semistrictly C-quasiconvex functions by means of scalar semistrictly quasiconvex functions that are compositions of the nonlinear scalarization functions introduced by Gerstewitz (Tammer) in 1983 with the initial vector function. In light of this characterization, the new concept of semistrict C-quasiconvexity seems to be a natural vector counterpart for the scalar concept of semistrict quasiconvexity.
AB - We establish a new concept of semistrict quasiconvexity for vector functions defined on a nonempty convex set in a real linear space X that take values in some real topological linear space Y, partially ordered by a proper solid convex cone C. The so-called semistrict C-quasiconvexity notion recovers the classical concept of semistrict quasiconvexity of scalar functions when (Formula presented.) and (Formula presented.). Additionally, analogous to the scalar scenario, if the cone C is closed, a vector function is both semistrictly C-quasiconvex and C-quasiconvex (in the sense of Luc, 1989) if and only if it is explicitly C-quasiconvex (in the sense of Popovici, 2007). Finally, we convey a characterization of semistrictly C-quasiconvex functions by means of scalar semistrictly quasiconvex functions that are compositions of the nonlinear scalarization functions introduced by Gerstewitz (Tammer) in 1983 with the initial vector function. In light of this characterization, the new concept of semistrict C-quasiconvexity seems to be a natural vector counterpart for the scalar concept of semistrict quasiconvexity.
KW - Generalized convexity
KW - nonlinear scalarization function
KW - vector function
UR - http://www.scopus.com/inward/record.url?scp=85200266301&partnerID=8YFLogxK
U2 - 10.1080/02331934.2024.2384919
DO - 10.1080/02331934.2024.2384919
M3 - Article
JO - OPTIMIZATION
JF - OPTIMIZATION
SN - 0323-3898
ER -