IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v22y2024i1d10.1007_s10288-023-00541-9.html
   My bibliography  Save this article

Derivative-free separable quadratic modeling and cubic regularization for unconstrained optimization

Author

Listed:
  • A. L. Custódio

    (FCT NOVA
    FCT NOVA)

  • R. Garmanjani

    (FCT NOVA)

  • M. Raydan

    (FCT NOVA)

Abstract

We present a derivative-free separable quadratic modeling and cubic regularization technique for solving smooth unconstrained minimization problems. The derivative-free approach is mainly concerned with building a quadratic model that could be generated by numerical interpolation or using a minimum Frobenius norm approach, when the number of points available does not allow to build a complete quadratic model. This model plays a key role to generate an approximated gradient vector and Hessian matrix of the objective function at every iteration. We add a specialized cubic regularization strategy to minimize the quadratic model at each iteration, that makes use of separability. We discuss convergence results, including worst case complexity, of the proposed schemes to first-order stationary points. Some preliminary numerical results are presented to illustrate the robustness of the specialized separable cubic algorithm.

Suggested Citation

  • A. L. Custódio & R. Garmanjani & M. Raydan, 2024. "Derivative-free separable quadratic modeling and cubic regularization for unconstrained optimization," 4OR, Springer, vol. 22(1), pages 121-144, March.
    • Handle: RePEc:spr:aqjoor:v:22:y:2024:i:1:d:10.1007_s10288-023-00541-9
    DOI: 10.1007/s10288-023-00541-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-023-00541-9
    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/s10288-023-00541-9?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:aqjoor:v:22:y:2024:i:1:d:10.1007_s10288-023-00541-9. 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.