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Titel: Vector optimization w.r.t. relatively solid convex cones in real linear spaces
Autor(en): Günther, Christian
Khazayel, Bahareh
Tammer, Christiane
Erscheinungsdatum: 2021
Art: Artikel
Sprache: Englisch
Zusammenfassung: In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) is preordered by a not necessarily solid (and not necessarily pointed) convex cone. It is well-known that there are many examples where the ordering cone of the image space has an empty (topological/algebraic) interior, for instance in optimal control, approximation theory, duality theory. Our aim is to consider Pareto-type solution concepts for such vector optimization problems based on the intrinsic core notion (a well-known generalized interiority notion). We propose a new Henig-type proper efficiency concept based on generalized dilating cones which are relatively solid (i.e., their intrinsic cores are nonempty). Using linear functionals from the dual cone of the ordering cone, we are able to characterize the sets of (weakly, properly) efficient solutions under certain generalized convexity assumptions. Toward this end, we employ separation theorems that are working in the considered setting.
URI: https://opendata.uni-halle.de//handle/1981185920/65136
http://dx.doi.org/10.25673/63185
Open-Access: Open-Access-Publikation
Nutzungslizenz: (CC BY 4.0) Creative Commons Namensnennung 4.0 International(CC BY 4.0) Creative Commons Namensnennung 4.0 International
Sponsor/Geldgeber: Publikationsfonds MLU
Journal Titel: Journal of Optimization Theory and Applications
Verlag: Springer Science + Business Media
Verlagsort: Dordrecht [u.a.]
Originalveröffentlichung: 10.1007/s10957-021-01976-y
Enthalten in den Sammlungen:Open Access Publikationen der MLU

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