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

authored by

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.

Organisation(s)

Institute of Applied Mathematics

External Organisation(s)

Martin Luther University Halle-Wittenberg

Type

Article

Journal

Minimax Theory and its Applications

Volume

9

Pages

225-252

No. of pages

28

ISSN

2199-1413

Publication date

10.2024

Publication status

Published

Peer reviewed

Yes

Electronic version(s)

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