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

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Christian Günther
  • Bahareh Khazayel
  • Christiane Tammer

Organisationseinheiten

Externe Organisationen

  • Martin-Luther-Universität Halle-Wittenberg
Forschungs-netzwerk anzeigen

Details

OriginalspracheDeutsch
Seiten (von - bis)225-252
Seitenumfang28
FachzeitschriftMinimax Theory and its Applications
Jahrgang9
Ausgabenummer8
PublikationsstatusVeröffentlicht - Okt. 2024

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.

Zitieren

Duality Assertions in Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces. / Günther, Christian; Khazayel, Bahareh; Tammer, Christiane.
in: Minimax Theory and its Applications, Jahrgang 9, Nr. 8, 10.2024, S. 225-252.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Günther, C, Khazayel, B & Tammer, C 2024, 'Duality Assertions in Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces', Minimax Theory and its Applications, Jg. 9, Nr. 8, S. 225-252. <https://www.heldermann-verlag.de/mta/mta09/mta0180-b.pdf>
Günther, C., Khazayel, B., & Tammer, C. (2024). Duality Assertions in Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces. Minimax Theory and its Applications, 9(8), 225-252. https://www.heldermann-verlag.de/mta/mta09/mta0180-b.pdf
Günther C, Khazayel B, Tammer C. Duality Assertions in Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces. Minimax Theory and its Applications. 2024 Okt;9(8):225-252.
Günther, Christian ; Khazayel, Bahareh ; Tammer, Christiane. / Duality Assertions in Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces. in: Minimax Theory and its Applications. 2024 ; Jahrgang 9, Nr. 8. S. 225-252.
Download
@article{00ca31108eb24232abe331537a10077b,
title = "Duality Assertions in Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces",
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. ",
author = "Christian G{\"u}nther and Bahareh Khazayel and Christiane Tammer",
year = "2024",
month = oct,
language = "Deutsch",
volume = "9",
pages = "225--252",
number = "8",

}

Download

TY - JOUR

T1 - Duality Assertions in Vector Optimization w.r.t. Relatively Solid Convex Cones in Real Linear Spaces

AU - Günther, Christian

AU - Khazayel, Bahareh

AU - Tammer, Christiane

PY - 2024/10

Y1 - 2024/10

N2 - 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.

AB - 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.

M3 - Artikel

VL - 9

SP - 225

EP - 252

JO - Minimax Theory and its Applications

JF - Minimax Theory and its Applications

SN - 2199-1413

IS - 8

ER -