IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v32y2015i01ns0217595915400084.html
   My bibliography  Save this article

A Splitting Augmented Lagrangian Method for Low Multilinear-Rank Tensor Recovery

Author

Listed:
  • Lei Yang

    (Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P. R. China)

  • Zheng-Hai Huang

    (Center for Applied Mathematics of Tianjin University, Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P. R. China)

  • Yu-Fan Li

    (Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, P. R. China)

Abstract

This paper studies a recovery task of finding a low multilinear-rank tensor that fulfills some linear constraints in the general settings, which has many applications in computer vision and graphics. This problem is named as the low multilinear-rank tensor recovery problem. The variable splitting technique and convex relaxation technique are used to transform this problem into a tractable constrained optimization problem. Considering the favorable structure of the problem, we develop a splitting augmented Lagrangian method (SALM) to solve the resulting problem. The proposed algorithm is easily implemented and its convergence can be proved under some conditions. Some preliminary numerical results on randomly generated and real completion problems show that the proposed algorithm is very effective and robust for tackling the low multilinear-rank tensor completion problem.

Suggested Citation

  • Lei Yang & Zheng-Hai Huang & Yu-Fan Li, 2015. "A Splitting Augmented Lagrangian Method for Low Multilinear-Rank Tensor Recovery," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(01), pages 1-25.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:01:n:s0217595915400084
    DOI: 10.1142/S0217595915400084
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595915400084
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595915400084?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.

    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:wsi:apjorx:v:32:y:2015:i:01:n:s0217595915400084. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.