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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Vydáno v:European journal of operational research Ročník 210; číslo 2; s. 158 - 168
Hlavní autor: Luc, Dinh The
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 16.04.2011
Elsevier
Elsevier Sequoia S.A
Edice:European Journal of Operational Research
Témata:
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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Popis
Shrnutí: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.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2010.09.024