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Title: Vector optimization w.r.t. relatively solid convex cones in real linear spaces
Author(s): Günther, Christian
Khazayel, Bahareh
Tammer, Christiane
Issue Date: 2021
Type: Article
Language: English
Abstract: 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.
Open Access: Open access publication
License: (CC BY 4.0) Creative Commons Attribution 4.0(CC BY 4.0) Creative Commons Attribution 4.0
Sponsor/Funder: Publikationsfonds MLU
Journal Title: Journal of Optimization Theory and Applications
Publisher: Springer Science + Business Media
Publisher Place: Dordrecht [u.a.]
Original Publication: 10.1007/s10957-021-01976-y
Appears in Collections:Open Access Publikationen der MLU

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