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Journal of Convex Analysis 11 (2004), No. 1, 163--178
Copyright Heldermann Verlag 2004

Closing the Duality Gap in Linear Vector Optimization

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

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.

Keywords: set-valued optimization, duality, linear multicriteria optimization.

MSC: 90C29, 90C46, 90C05.

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