Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces

Christian Günther (), Bahareh Khazayel () and Christiane Tammer ()
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Christian Günther: Martin Luther University Halle-Wittenberg
Bahareh Khazayel: Martin Luther University Halle-Wittenberg
Christiane Tammer: Martin Luther University Halle-Wittenberg

Journal of Optimization Theory and Applications, 2022, vol. 193, issue 1, No 19, 408-442

Abstract: 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.

Keywords: Vector optimization; Relatively solid convex cone; Intrinsic core; (Weak) Pareto efficiency; Henig proper efficiency; Generalized dilating cones; Scalarization; Separation theorem; 90C48; 90C29; 06F20; 52A05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10957-021-01976-y

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