IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v59y2004i1p69-89.html
   My bibliography  Save this article

Gap-free computation of Pareto-points by quadratic scalarizations

Author

Listed:
  • Jörg Fliege

Abstract

In multicriteria optimization, several objective functions have to be minimized simultaneously. For this kind of problem, approximations to the whole solution set are of particular importance to decision makers. Usually, approximating this set involves solving a family of parameterized optimization problems. It is the aim of this paper to argue in favour of parameterized quadratic objective functions, in contrast to the standard weighting approach in which parameterized linear objective functions are used. These arguments will rest on the favourable numerical properties of these quadratic scalarizations, which will be investigated in detail. Moreover, it will be shown which parameter sets can be used to recover all solutions of an original multiobjective problem where the ordering in the image space is induced by an arbitrary convex cone. Copyright Springer-Verlag 2004

Suggested Citation

  • Jörg Fliege, 2004. "Gap-free computation of Pareto-points by quadratic scalarizations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(1), pages 69-89, February.
    • Handle: RePEc:spr:mathme:v:59:y:2004:i:1:p:69-89
    DOI: 10.1007/s001860300316
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s001860300316
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s001860300316?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    Citations

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


    Cited by:

    1. J. Fliege & L. N. Vicente, 2006. "Multicriteria Approach to Bilevel Optimization," Journal of Optimization Theory and Applications, Springer, vol. 131(2), pages 209-225, November.
    2. Fliege, Jörg & Werner, Ralf, 2014. "Robust multiobjective optimization & applications in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 422-433.
    3. Vahid Morovati & Hadi Basirzadeh & Latif Pourkarimi, 2018. "Quasi-Newton methods for multiobjective optimization problems," 4OR, Springer, vol. 16(3), pages 261-294, September.
    4. Jörg Fliege, 2006. "An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 825-845, November.
    5. Jörg Fliege & Huifu Xu, 2011. "Stochastic Multiobjective Optimization: Sample Average Approximation and Applications," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 135-162, October.
    6. G. Cocchi & M. Lapucci, 2020. "An augmented Lagrangian algorithm for multi-objective optimization," Computational Optimization and Applications, Springer, vol. 77(1), pages 29-56, September.
    7. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "A Semidefinite Programming approach for solving Multiobjective Linear Programming," Journal of Global Optimization, Springer, vol. 58(3), pages 465-480, March.
    8. Johan M. Bogoya & Andrés Vargas & Oliver Schütze, 2019. "The Averaged Hausdorff Distances in Multi-Objective Optimization: A Review," Mathematics, MDPI, vol. 7(10), pages 1-35, September.

    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:spr:mathme:v:59:y:2004:i:1:p:69-89. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.