A new concept of semistrict quasiconvexity for vector functions

verfasst von: Christian Günther, Alexandru Orzan, Nicolae Popovici
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.
Organisationseinheit(en): Institut für Angewandte Mathematik
Typ: Artikel
Journal: OPTIMIZATION
ISSN: 0323-3898
Publikationsdatum: 08.2024
Publikationsstatus: Elektronisch veröffentlicht (E-Pub)
Peer-reviewed: Ja
ASJC Scopus Sachgebiete: Steuerung und Optimierung, Angewandte Mathematik, Managementlehre und Operations Resarch
Elektronische Version(en): https://doi.org/10.1080/02331934.2024.2384919 (Zugang: Offen)

BibTeX

@article{89a09f4ff4f84a50b26f423a3d308dfa,
title = "A new concept of semistrict quasiconvexity for vector functions",
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",
author = "Christian G{\"u}nther and Alexandru Orzan and Nicolae Popovici",
note = "Publisher Copyright: {\textcopyright} 2024 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.",
year = "2024",
month = aug,
doi = "10.1080/02331934.2024.2384919",
language = "English",
journal = "OPTIMIZATION",
issn = "0323-3898",
publisher = "Taylor and Francis Ltd.",
}