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

verfasst von

Christian Günther, Bahareh Khazayel, Christiane Tammer

Abstract

We derive duality assertions for vector optimization problems in real linear spaces based on a scalarization using recent results concerning the concept of relative solidness for convex cones (i.e., convex cones with nonempty intrinsic cores). In our paper, we consider an abstract vector optimization problem with generalized inequality constraints and investigate Lagrangian type duality assertions for (weak, proper) minimality notions. Our interest is neither to impose a pointedness assumption nor a solidness assumption for the convex cones involved in the solution concept of the vector optimization problem. We are able to extend the well-known Lagrangian vector duality approach by J. Jahn [Duality in vector optimization, Math. Programming 25 (1983) 343--353] to such a setting.

Organisationseinheit(en)

Institut für Angewandte Mathematik

Externe Organisation(en)

Martin-Luther-Universität Halle-Wittenberg

Typ

Artikel

Journal

Minimax Theory and its Applications

Band

9

Seiten

225-252

Anzahl der Seiten

28

ISSN

2199-1413

Publikationsdatum

10.2024

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

Elektronische Version(en)

https://www.heldermann-verlag.de/mta/mta09/mta0180-b.pdf (Zugang: Geschlossen)