IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v90y2025i2d10.1007_s10589-024-00634-z.html
   My bibliography  Save this article

Rank-one approximation of a higher-order tensor by a Riemannian trust-region method

Author

Listed:
  • Jianheng Chen

    (Zhejiang University of Water Resources and Electric Power
    Xiamen University)

  • Wen Huang

    (Xiamen University)

Abstract

In this paper, we consider a rank-one approximation problem of a higher-order tensor. We treat the problem as an optimization model on a Cartesian product of manifolds and solve this model by using a Riemannian optimization method. We derive the action of the Riemannian Hessian of the objective function on tangent vectors to the Cartesian product of manifolds. A Riemannian trust-region method with block-diagonal Hessian is used to solve this model, and the subproblem is solved by the truncated conjugate gradient method. The convergence analysis of the Riemannian trust-region method has been established in the literature with certain assumptions. We verify those assumptions for the rank-one approximation problem. Numerical experiments illustrate that the proposed model with the method is feasible and effective.

Suggested Citation

  • Jianheng Chen & Wen Huang, 2025. "Rank-one approximation of a higher-order tensor by a Riemannian trust-region method," Computational Optimization and Applications, Springer, vol. 90(2), pages 515-556, March.
    • Handle: RePEc:spr:coopap:v:90:y:2025:i:2:d:10.1007_s10589-024-00634-z
    DOI: 10.1007/s10589-024-00634-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-024-00634-z
    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/s10589-024-00634-z?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:spr:coopap:v:90:y:2025:i:2:d:10.1007_s10589-024-00634-z. 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: 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.