On duality in multiple objective linear programming

In this paper we present two approaches to duality in multiple objective linear programming. The first approach is based on a duality relation between maximal elements of a set and minimal elements of its complement. It offers a general duality scheme which unifies a number of known dual constructio...

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Veröffentlicht in:	European journal of operational research Jg. 210; H. 2; S. 158 - 168
1. Verfasser:	Luc, Dinh The
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Amsterdam Elsevier B.V 16.04.2011 Elsevier Elsevier Sequoia S.A
Schriftenreihe:	European Journal of Operational Research
Schlagworte:	Applied sciences Complement Construction Decision theory. Utility theory Duality Exact sciences and technology Linear programming Mathematical programming Mathematics Multiple objective Multiple objective linear problem Multiple objective linear problem Duality Normal cone Normal cone Operational research Operational research and scientific management Operational research. Management science Optimization Polarity Studies Multiple objective linear problem Normal cone Duality Polyhedron Cone Convex set Multiobjective programming Linear programming
ISSN:	0377-2217, 1872-6860
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Abstract	In this paper we present two approaches to duality in multiple objective linear programming. The first approach is based on a duality relation between maximal elements of a set and minimal elements of its complement. It offers a general duality scheme which unifies a number of known dual constructions and improves several existing duality relations. The second approach utilizes polarity between a convex polyhedral set and the epigraph of its support function. It leads to a parametric dual problem and yields strong duality relations, including those of geometric duality.
AbstractList	In this paper we present two approaches to duality in multiple objective linear programming. The first approach is based on a duality relation between maximal elements of a set and minimal elements of its complement. It offers a general duality scheme which unifies a number of known dual constructions and improves several existing duality relations. The second approach utilizes polarity between a convex polyhedral set and the epigraph of its support function. It leads to a parametric dual problem and yields strong duality relations, including those of geometric duality. In this paper we present two approaches to duality in multiple objective linear programming. The first approach is based on a duality relation between maximal elements of a set and minimal elements of its complement. It offers a general duality scheme which unifies a number of known dual constructions and improves several existing duality relations. The second approach utilizes polarity between a convex polyhedral set and the epigraph of its support function. It leads to a parametric dual problem and yields strong duality relations, including those of geometric duality. [PUBLICATION ABSTRACT]
Author	Luc, Dinh The
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Keywords	Multiple objective linear problem Normal cone Duality Polyhedron Cone Convex set Multiobjective programming Linear programming
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SubjectTerms	Applied sciences Complement Construction Decision theory. Utility theory Duality Exact sciences and technology Linear programming Mathematical programming Mathematics Multiple objective Multiple objective linear problem Multiple objective linear problem Duality Normal cone Normal cone Operational research Operational research and scientific management Operational research. Management science Optimization Polarity Studies
Title	On duality in multiple objective linear programming
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