IDEAS home Printed from https://ideas.repec.org/p/cor/louvrp/600.html
   My bibliography  Save this paper

On efficient solutions to multiple objective mathematical programs

Author

Listed:
  • LOWE, T.J.
  • THISSE, J.-F.
  • WARD, J.E.
  • WENDELL, R.E.

Abstract

This note develops properties of quasi-efficient solutions and explores interrelationships to the classical concept of efficiency. In particular, a point is a quasi-efficient solution to a multiple objective mathematical program if and only if it is an optimal solution to a scalar maximum problem for some set of nonnegative weights on the objectives. This result is then used to characterize the set of quasi-efficient solutions as the union of efficient solutions to a multiple objective problem over all nonempty subsets of the objectives.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Lowe, T.J. & Thisse, J.-F. & Ward, J.E. & Wendell, R.E., 1984. "On efficient solutions to multiple objective mathematical programs," LIDAM Reprints CORE 600, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:600
    DOI: 10.1287/mnsc.30.11.1346
    Note: In : Management Science, 30(11), 1346-1349, 1984
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    Citations

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


    Cited by:

    1. Alexander Engau & Margaret M. Wiecek, 2008. "Interactive Coordination of Objective Decompositions in Multiobjective Programming," Management Science, INFORMS, vol. 54(7), pages 1350-1363, July.
    2. Psarras, J. & Capros, P. & Samouilidis, J.-E., 1990. "4.5. Multiobjective programming," Energy, Elsevier, vol. 15(7), pages 583-605.
    3. Bennet Gebken & Sebastian Peitz & Michael Dellnitz, 2019. "On the hierarchical structure of Pareto critical sets," Journal of Global Optimization, Springer, vol. 73(4), pages 891-913, April.
    4. Alzorba, Shaghaf & Günther, Christian & Popovici, Nicolae & Tammer, Christiane, 2017. "A new algorithm for solving planar multiobjective location problems involving the Manhattan norm," European Journal of Operational Research, Elsevier, vol. 258(1), pages 35-46.
    5. Jornada, Daniel & Leon, V. Jorge, 2016. "Biobjective robust optimization over the efficient set for Pareto set reduction," European Journal of Operational Research, Elsevier, vol. 252(2), pages 573-586.
    6. Naoki Hamada & Shunsuke Ichiki, 2022. "Free Disposal Hull Condition to Verify When Efficiency Coincides with Weak Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 248-270, January.
    7. Nicolae Popovici, 2017. "A decomposition approach to vector equilibrium problems," Annals of Operations Research, Springer, vol. 251(1), pages 105-115, April.
    8. Lindroth, Peter & Patriksson, Michael & Strömberg, Ann-Brith, 2010. "Approximating the Pareto optimal set using a reduced set of objective functions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1519-1534, December.
    9. Nicolae Popovici & Matteo Rocca, 2010. "Pareto reducibility of vector variational inequalities," Economics and Quantitative Methods qf1004, Department of Economics, University of Insubria.
    10. Francisco Ruiz & Lourdes Rey & María Muñoz, 2008. "A graphical characterization of the efficient set for convex multiobjective problems," Annals of Operations Research, Springer, vol. 164(1), pages 115-126, November.

    More about this item

    Statistics

    Access and download statistics

    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:cor:louvrp:600. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Alain GILLIS (email available below). General contact details of provider: https://edirc.repec.org/data/coreebe.html .

    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.