IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v210y2011i2p158-168.html
   My bibliography  Save this article

On duality in multiple objective linear programming

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00622-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Luis Rodríguez-Marín & Miguel Sama, 2013. "Scalar Lagrange Multiplier Rules for Set-Valued Problems in Infinite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 156(3), pages 683-700, March.
    3. B. Jiménez & V. Novo & A. Vílchez, 2020. "Characterization of set relations through extensions of the oriented distance," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 89-115, February.
    4. Hernández-Lerma, Onésimo & Romera, Rosario, 2000. "Pareto optimality in multiobjective Markov control processes," DES - Working Papers. Statistics and Econometrics. WS 9865, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. 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.
    6. Balbás, Alejandro & Balbás, Raquel & Mayoral, Silvia, 2009. "Portfolio choice and optimal hedging with general risk functions: A simplex-like algorithm," European Journal of Operational Research, Elsevier, vol. 192(2), pages 603-620, January.
    7. A. Balbás & E. Galperin & P. Jiménez-Guerra, 2002. "Radial Solutions and Orthogonal Trajectories in Multiobjective Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 115(2), pages 315-344, November.
    8. Andreas H Hamel & Andreas Löhne, 2020. "Choosing sets: preface to the special issue on set optimization and applications," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 1-4, February.
    9. Tijani Amahroq & Abdessamad Oussarhan, 2019. "Lagrange Multiplier Rules for Weakly Minimal Solutions of Compact-Valued Set Optimization Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(04), pages 1-22, August.
    10. Muñoz-Bouzo, María José, 1997. "Stochastic measures of financial markets efficiency and integration," DEE - Working Papers. Business Economics. WB 7018, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:210:y:2011:i:2:p:158-168. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.