IDEAS home Printed from https://ideas.repec.org/p/cor/louvrp/3166.html
   My bibliography  Save this paper

Lower bounds on the nonnegative rank using a nested polytopes formulation

Author

Listed:
  • Dewez, Julien

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

  • Glineur, François

    (Université catholique de Louvain, LIDAM/CORE, Belgium)

Abstract

Computing the nonnegative rank of a nonnegative matrix has been proven to be, in general, NP-hard. However, this quantity has many interesting applications, e.g., it can be used to compute the ex- tension complexity of polytopes. Therefore researchers have been trying to approximate this quantity as closely as possible with strong lower and upper bounds. In this work, we introduce a new lower bound on the nonnegative rank based on a representation of the matrix as a pair of nested polytopes. The nonnegative rank then corresponds to the minimum num-er of vertices of any polytope nested between these two polytopes. Using the geometric concept of supporting corner, we introduce a parametrized family of computable lower bounds and present preliminary numerical results on slack matrices of regular polygons.

Suggested Citation

  • Dewez, Julien & Glineur, François, 2021. "Lower bounds on the nonnegative rank using a nested polytopes formulation," LIDAM Reprints CORE 3166, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:3166
    Note: In: ESANN2020, 28th European Symposium on Artificial Neural Networks - Computational Intelligence and Machine Learning, 2020
    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.

    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:3166. 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.