IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v155y2012i2d10.1007_s10957-012-0069-7.html
   My bibliography  Save this article

Beyond Canonical DC-Optimization: The Single Reverse Polar Problem

Author

Listed:
  • Giancarlo Bigi

    (Università di Pisa)

  • Antonio Frangioni

    (Università di Pisa)

  • Qinghua Zhang

    (Wuhan University)

Abstract

We propose a novel generalization of the Canonical Difference of Convex problem (CDC), and we study the convergence of outer approximation algorithms for its solution, which use an approximated oracle for checking the global optimality conditions. Although the approximated optimality conditions are similar to those of CDC, this new class of problems is shown to significantly differ from its special case. Indeed, outer approximation approaches for CDC need be substantially modified in order to cope with the more general problem, bringing to new algorithms. We develop a hierarchy of conditions that guarantee global convergence, and we build three different cutting plane algorithms relying on them.

Suggested Citation

  • Giancarlo Bigi & Antonio Frangioni & Qinghua Zhang, 2012. "Beyond Canonical DC-Optimization: The Single Reverse Polar Problem," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 430-452, November.
    • Handle: RePEc:spr:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0069-7
    DOI: 10.1007/s10957-012-0069-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-012-0069-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-012-0069-7?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.

    References listed on IDEAS

    as
    1. Rafael Blanquero & Emilio Carrizosa & Pierre Hansen, 2009. "Locating Objects in the Plane Using Global Optimization Techniques," Mathematics of Operations Research, INFORMS, vol. 34(4), pages 837-858, November.
    2. Giancarlo Bigi & Antonio Frangioni & Qinghua Zhang, 2010. "Outer approximation algorithms for canonical DC problems," Journal of Global Optimization, Springer, vol. 46(2), pages 163-189, February.
    3. Fulop, Janos, 1990. "A finite cutting plane method for solving linear programs with an additional reverse convex constraint," European Journal of Operational Research, Elsevier, vol. 44(3), pages 395-409, February.
    Full references (including those not matched with items on IDEAS)

    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. Qinghua Zhang, 2013. "A new necessary and sufficient global optimality condition for canonical DC problems," Journal of Global Optimization, Springer, vol. 55(3), pages 559-577, March.
    2. M. V. Dolgopolik, 2020. "New global optimality conditions for nonsmooth DC optimization problems," Journal of Global Optimization, Springer, vol. 76(1), pages 25-55, January.
    3. Schöbel, Anita & Scholz, Daniel, 2014. "A solution algorithm for non-convex mixed integer optimization problems with only few continuous variables," European Journal of Operational Research, Elsevier, vol. 232(2), pages 266-275.
    4. Giancarlo Bigi & Antonio Frangioni & Qinghua Zhang, 2010. "Outer approximation algorithms for canonical DC problems," Journal of Global Optimization, Springer, vol. 46(2), pages 163-189, February.
    5. Blanquero, Rafael & Carrizosa, Emilio & Schöbel, Anita & Scholz, Daniel, 2011. "A global optimization procedure for the location of a median line in the three-dimensional space," European Journal of Operational Research, Elsevier, vol. 215(1), pages 14-20, November.
    6. Carrizosa, Emilio & Goerigk, Marc & Schöbel, Anita, 2017. "A biobjective approach to recoverable robustness based on location planning," European Journal of Operational Research, Elsevier, vol. 261(2), pages 421-435.
    7. Rafael Blanquero & Emilio Carrizosa, 2013. "Solving the median problem with continuous demand on a network," Computational Optimization and Applications, Springer, vol. 56(3), pages 723-734, December.

    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:joptap:v:155:y:2012:i:2:d:10.1007_s10957-012-0069-7. 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: 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.