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

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Christian Günther
  • Bahareh Khazayel
  • Christiane Tammer

Research Organisations

External Research Organisations

  • Martin Luther University Halle-Wittenberg

Details

Original languageGerman
Pages (from-to)225-252
Number of pages28
JournalMinimax Theory and its Applications
Volume9
Issue number8
Publication statusPublished - Oct 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.

Keywords

    Vector optimization, efficiency, intrinsic core, minimality, regularity, relatively solid convex cones, strong duality, weak duality

ASJC Scopus subject areas

Cite this

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, Vol. 9, No. 8, 10.2024, p. 225-252.

Research output: Contribution to journal › Article › Research › 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, vol. 9, no. 8, pp. 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 Oct;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 ; Vol. 9, No. 8. pp. 225-252.
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AU - Günther, Christian

AU - Khazayel, Bahareh

AU - Tammer, Christiane

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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.

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KW - Vector optimization

KW - efficiency

KW - intrinsic core

KW - minimality

KW - regularity

KW - relatively solid convex cones

KW - strong duality

KW - weak duality

M3 - Artikel

VL - 9

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EP - 252

JO - Minimax Theory and its Applications

JF - Minimax Theory and its Applications

SN - 2199-1413

IS - 8

ER -