
Minimax Theory and its Applications 09 (2024), No. 2, 225252 Copyright Heldermann Verlag 2024 Duality Assertions in Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces Christian Günther Institut für Angewandte Mathematik, Leibniz Universität, Hannover, Germany c.guenther@ifam.unihannover.de Bahareh Khazayel Institute of Mathematics, Martin Luther University, HalleWittenberg, Germany bahareh.khazayel@mathematik.unihalle.de Christiane Tammer Institute of Mathematics, Martin Luther University, HalleWittenberg, Germany christiane.tammer@mathematik.unihalle.de 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 wellknown Lagrangian vector duality approach by J. Jahn [Duality in vector optimization, Math. Programming 25 (1983) 343353] to such a setting. Keywords: Vector optimization, relatively solid convex cones, intrinsic core, minimality, efficiency, weak duality, strong duality, regularity. MSC: 90C48, 90C29, 06F20, 52A05, 49N15. [ Fulltextpdf (173 KB)] for subscribers only. 