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On duality in multiple objective linear programming

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  • Luc, Dinh The

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.

Suggested Citation

  • Luc, Dinh The, 2011. "On duality in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 210(2), pages 158-168, April.
    • Handle: RePEc:eee:ejores:v:210:y:2011:i:2:p:158-168
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    References listed on IDEAS

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    1. E. Galperin & P. Jimenez Guerra, 2001. "Duality of Nonscalarized Multiobjective Linear Programs: Dual Balance, Level Sets, and Dual Clusters of Optimal Vectors," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 109-137, January.
    2. Frank Heyde & Andreas Löhne & Christiane Tammer, 2009. "Set-valued duality theory for multiple objective linear programs and application to mathematical finance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(1), pages 159-179, March.
    3. Balbas, Alejandro & Heras, Antonio, 1993. "Duality theory for infinite-dimensional multiobjective linear programming," European Journal of Operational Research, Elsevier, vol. 68(3), pages 379-388, August.
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    Cited by:

    1. N. Mahdavi-Amiri & F. Salehi Sadaghiani, 2017. "Strictly feasible solutions and strict complementarity in multiple objective linear optimization," 4OR, Springer, vol. 15(3), pages 303-326, September.
    2. Andreas Hamel & Andreas Löhne & Birgit Rudloff, 2014. "Benson type algorithms for linear vector optimization and applications," Journal of Global Optimization, Springer, vol. 59(4), pages 811-836, August.
    3. Daniel Gourion & Dinh Luc, 2014. "Saddle points and scalarizing sets in multiple objective linear programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 1-27, August.

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