Geometric Duality in Multiple Objective Linear Programming

We develop in this article a geometric approach to duality in multiple objective linear programming. This approach is based on a very old idea, the duality of polytopes, which can be traced back to the old Greeks. We show that there is an inclusion-reversing one-to-one map between the minimal faces...

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Bibliographic Details
Published in:SIAM journal on optimization Vol. 19; no. 2; pp. 836 - 845
Main Authors: Heyde, Frank, Löhne, Andreas
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2008
Subjects:
Linear programming
Optimization
Polytopes
ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary:We develop in this article a geometric approach to duality in multiple objective linear programming. This approach is based on a very old idea, the duality of polytopes, which can be traced back to the old Greeks. We show that there is an inclusion-reversing one-to-one map between the minimal faces of the image of the primal objective and the maximal faces of the image of the dual objective map.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:1052-6234
1095-7189
DOI:10.1137/060674831