Abstract

Using a set-valued dual cost function we give a new approach to duality theory for linear vector optimization problems. We develop the theory very close to the scalar case. Especially, in contrast to known results, we avoid the appearance of a duality gap in case of b = 0. Examples are given.

Author information

Contact details are reproduced from the original publication and may be historical.

Andreas H. Hamel

Martin-Luther-University Halle-Wittenberg, Dept. of Mathematics and Computer Science,
Theodor-Lieser-Str. 5, 06099 Halle, Germany

hamel@mathematik.uni-halle.de

Frank Heyde

Martin-Luther-University Halle-Wittenberg, Dept. of Mathematics and Computer Science,
Theodor-Lieser-Str. 5, 06099 Halle, Germany

Andreas Löhne

Martin-Luther-University Halle-Wittenberg, Dept. of Mathematics and Computer Science,
Theodor-Lieser-Str. 5, 06099 Halle, Germany

Christiane Tammer

Martin-Luther-University Halle-Wittenberg, Dept. of Mathematics and Computer Science,
Theodor-Lieser-Str. 5, 06099 Halle, Germany

Kristin Winkler

Martin-Luther-University Halle-Wittenberg, Dept. of Mathematics and Computer Science,
Theodor-Lieser-Str. 5, 06099 Halle, Germany

Keywords

  • set-valued optimization
  • duality
  • linear multicriteria optimization

Mathematics Subject Classification

90C29, 90C46, 90C05

Suggested citation

A. H. Hamel, F. Heyde, A. Löhne, Ch. Tammer, K. Winkler. “Closing the Duality Gap in Linear Vector Optimization.” Journal of Convex Analysis 11 (2004), No. 1, 163–178. https://doi.org/10.68381/jca11011

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 2004. Rights now held by Banach Press.