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.

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

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.