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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.
AH
Andreas H. Hamel
Martin-Luther-University Halle-Wittenberg, Dept. of Mathematics and Computer Science, Theodor-Lieser-Str. 5, 06099 Halle, Germany
Martin-Luther-University Halle-Wittenberg, Dept. of Mathematics and Computer Science, Theodor-Lieser-Str. 5, 06099 Halle, Germany
AL
Andreas Löhne
Martin-Luther-University Halle-Wittenberg, Dept. of Mathematics and Computer Science, Theodor-Lieser-Str. 5, 06099 Halle, Germany
CT
Christiane Tammer
Martin-Luther-University Halle-Wittenberg, Dept. of Mathematics and Computer Science, Theodor-Lieser-Str. 5, 06099 Halle, Germany
KW
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.