IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v60y2014i2p307-315.html
   My bibliography  Save this article

Optimal rank-sparsity decomposition

Author

Listed:
  • Jon Lee
  • Bai Zou

Abstract

We describe a branch-and-bound (b&b) method aimed at searching for an exact solution of the fundamental problem of decomposing a matrix into the sum of a sparse matrix and a low-rank matrix. Previous heuristic techniques employed convex and nonconvex optimization. We leverage and extend those ideas, within a spatial b&b framework, aimed at exact global optimization. Our work may serve to (i) gather evidence to assess the true quality of the previous heuristic techniques, and (ii) provide software to routinely calculate global optima or at least better solutions for moderate-sized instances coming from applications. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Jon Lee & Bai Zou, 2014. "Optimal rank-sparsity decomposition," Journal of Global Optimization, Springer, vol. 60(2), pages 307-315, October.
  • Handle: RePEc:spr:jglopt:v:60:y:2014:i:2:p:307-315
    DOI: 10.1007/s10898-013-0128-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-013-0128-0
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10898-013-0128-0?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. DE FARIAS, Ismael R. & NEMHAUSER, Georges L., 2003. "A polyhedral study of the cardinality constrained knapsack problem," LIDAM Reprints CORE 1634, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Elif Akçalı & Alper Üngör & Reha Uzsoy, 2005. "Short‐term capacity allocation problem with tool and setup constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(8), pages 754-764, December.
    2. F J Vasko & D D Newhart & A D Strauss, 2005. "Coal blending models for optimum cokemaking and blast furnace operation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(3), pages 235-243, March.
    3. Christopher Hojny & Tristan Gally & Oliver Habeck & Hendrik Lüthen & Frederic Matter & Marc E. Pfetsch & Andreas Schmitt, 2020. "Knapsack polytopes: a survey," Annals of Operations Research, Springer, vol. 292(1), pages 469-517, September.
    4. Joey Huchette & Joey Huchette, 2019. "A Combinatorial Approach for Small and Strong Formulations of Disjunctive Constraints," Mathematics of Operations Research, INFORMS, vol. 44(3), pages 793-820, August.
    5. Ahmet B. Keha & Ismael R. de Farias & George L. Nemhauser, 2006. "A Branch-and-Cut Algorithm Without Binary Variables for Nonconvex Piecewise Linear Optimization," Operations Research, INFORMS, vol. 54(5), pages 847-858, October.
    6. Young Woong Park & Diego Klabjan, 2020. "Subset selection for multiple linear regression via optimization," Journal of Global Optimization, Springer, vol. 77(3), pages 543-574, July.

    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:jglopt:v:60:y:2014:i:2:p:307-315. 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.