IDEAS home Printed from https://ideas.repec.org/p/cor/louvrp/1726.html
   My bibliography  Save this paper

Conic formulation for lp-norm optimization

Author

Listed:
  • GLINEUR, François
  • TERLAKY, Tamas

Abstract

In this paper, we formulate the l p -norm optimization problem as a conic optimization problem, derive its duality properties (weak duality, zero duality gap, and primal attainment) using standard conic duality and show how it can be solved in polynomial time applying the framework of interior-point algorithms based on self-concordant barriers.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • GLINEUR, François & TERLAKY, Tamas, 2004. "Conic formulation for lp-norm optimization," LIDAM Reprints CORE 1726, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:1726
    DOI: 10.1023/B:JOTA.0000042522.65261.51
    Note: In : Journal of Optimization Theory and Applications, 122(2), 285-307, 2004.
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1023/B:JOTA.0000042522.65261.51
    Download Restriction: no
    File URL: https://libkey.io/10.1023/B:JOTA.0000042522.65261.51?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
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. F. Glineur & T. Terlaky, 2004. "Conic Formulation for l p -Norm Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 285-307, August.
    2. François Glineur, 2001. "Proving Strong Duality for Geometric Optimization Using a Conic Formulation," Annals of Operations Research, Springer, vol. 105(1), pages 155-184, July.
    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. Robert Chares & François Glineur, 2008. "An interior-point method for the single-facility location problem with mixed norms using a conic formulation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 383-405, December.
    2. Yue Lu & Ching-Yu Yang & Jein-Shan Chen & Hou-Duo Qi, 2020. "The decompositions with respect to two core non-symmetric cones," Journal of Global Optimization, Springer, vol. 76(1), pages 155-188, January.
    3. Baha Alzalg, 2016. "The Algebraic Structure of the Arbitrary-Order Cone," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 32-49, April.
    4. Jinchuan Zhou & Yu-Lin Chang & Jein-Shan Chen, 2015. "The H-differentiability and calmness of circular cone functions," Journal of Global Optimization, Springer, vol. 63(4), pages 811-833, December.
    5. F. Glineur & T. Terlaky, 2004. "Conic Formulation for l p -Norm Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 285-307, August.
    6. Dávid Papp & Sercan Yıldız, 2022. "Alfonso: Matlab Package for Nonsymmetric Conic Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 11-19, January.
    7. Krokhmal, Pavlo A. & Soberanis, Policarpio, 2010. "Risk optimization with p-order conic constraints: A linear programming approach," European Journal of Operational Research, Elsevier, vol. 201(3), pages 653-671, March.

    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. Robert Chares & François Glineur, 2008. "An interior-point method for the single-facility location problem with mixed norms using a conic formulation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 383-405, December.
    2. Yue Lu & Ching-Yu Yang & Jein-Shan Chen & Hou-Duo Qi, 2020. "The decompositions with respect to two core non-symmetric cones," Journal of Global Optimization, Springer, vol. 76(1), pages 155-188, January.
    3. Krokhmal, Pavlo A. & Soberanis, Policarpio, 2010. "Risk optimization with p-order conic constraints: A linear programming approach," European Journal of Operational Research, Elsevier, vol. 201(3), pages 653-671, March.
    4. Jinchuan Zhou & Yu-Lin Chang & Jein-Shan Chen, 2015. "The H-differentiability and calmness of circular cone functions," Journal of Global Optimization, Springer, vol. 63(4), pages 811-833, December.
    5. Qinghong Zhang & Kenneth O. Kortanek, 2019. "On a Compound Duality Classification for Geometric Programming," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 711-728, March.
    6. Baha Alzalg, 2016. "The Algebraic Structure of the Arbitrary-Order Cone," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 32-49, April.
    7. Dávid Papp & Sercan Yıldız, 2022. "Alfonso: Matlab Package for Nonsymmetric Conic Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 11-19, January.

    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:1726. 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: 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.