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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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
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Abstract 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.
AbstractList 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.
Author Löhne, Andreas
Heyde, Frank
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Cites_doi 10.1007/BF01917642
10.1057/jors.1974.108
10.1023/A:1008215702611
10.1016/S0377-2217(77)81008-4
10.1287/moor.6.2.159
10.1080/02331930600819720
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Optimization
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Title Geometric Duality in Multiple Objective Linear Programming
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