Please use this identifier to cite or link to this item:
http://dx.doi.org/10.25673/63185
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. |
URI: | https://opendata.uni-halle.de//handle/1981185920/65136 http://dx.doi.org/10.25673/63185 |
Open Access: | Open access publication |
License: | (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 |
Files in This Item:
File | Description | Size | Format | |
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Günther2021_Article_VectorOptimizationWRTRelativel.pdf | 714.12 kB | Adobe PDF | View/Open |