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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Bibliographic Details
Published in:European journal of operational research Vol. 210; no. 2; pp. 158 - 168
Main Author: Luc, Dinh The
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.04.2011
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2010.09.024