IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v96y1998i3d10.1023_a1022608410710.html
   My bibliography  Save this article

Numerical Experience with a Class of Self-Scaling Quasi-Newton Algorithms

Author

Listed:
  • M. Al-Baali

    (UAE University)

Abstract

Self-scaling quasi-Newton methods for unconstrained optimization depend upon updating the Hessian approximation by a formula which depends on two parameters (say, τ and θ) such that τ = 1, θ = 0, and θ = 1 yield the unscaled Broyden family, the BFGS update, and the DFP update, respectively. In previous work, conditions were obtained on these parameters that imply global and superlinear convergence for self-scaling methods on convex objective functions. This paper discusses the practical performance of several new algorithms designed to satisfy these conditions.

Suggested Citation

  • M. Al-Baali, 1998. "Numerical Experience with a Class of Self-Scaling Quasi-Newton Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 533-553, March.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:3:d:10.1023_a:1022608410710
    DOI: 10.1023/A:1022608410710
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1022608410710
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1022608410710?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. Shmuel S. Oren & David G. Luenberger, 1974. "Self-Scaling Variable Metric (SSVM) Algorithms," Management Science, INFORMS, vol. 20(5), pages 845-862, January.
    2. Shmuel S. Oren, 1974. "Self-Scaling Variable Metric (SSVM) Algorithms," Management Science, INFORMS, vol. 20(5), pages 863-874, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. W. Y. Cheng & D. H. Li, 2010. "Spectral Scaling BFGS Method," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 305-319, August.
    2. Neculai Andrei, 2018. "A Double-Parameter Scaling Broyden–Fletcher–Goldfarb–Shanno Method Based on Minimizing the Measure Function of Byrd and Nocedal for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 191-218, July.

    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. Fahimeh Biglari & Farideh Mahmoodpur, 2016. "Scaling Damped Limited-Memory Updates for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 177-188, July.
    2. Nataj, Sarah & Lui, S.H., 2020. "Superlinear convergence of nonlinear conjugate gradient method and scaled memoryless BFGS method based on assumptions about the initial point," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    3. Martin Buhmann & Dirk Siegel, 2021. "Implementing and modifying Broyden class updates for large scale optimization," Computational Optimization and Applications, Springer, vol. 78(1), pages 181-203, January.
    4. C. X. Kou & Y. H. Dai, 2015. "A Modified Self-Scaling Memoryless Broyden–Fletcher–Goldfarb–Shanno Method for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 209-224, April.
    5. Saman Babaie-Kafaki, 2015. "On Optimality of the Parameters of Self-Scaling Memoryless Quasi-Newton Updating Formulae," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 91-101, October.
    6. S. Cipolla & C. Di Fiore & P. Zellini, 2020. "A variation of Broyden class methods using Householder adaptive transforms," Computational Optimization and Applications, Springer, vol. 77(2), pages 433-463, November.
    7. Saman Babaie-Kafaki & Reza Ghanbari, 2017. "A class of adaptive Dai–Liao conjugate gradient methods based on the scaled memoryless BFGS update," 4OR, Springer, vol. 15(1), pages 85-92, March.

    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:joptap:v:96:y:1998:i:3:d:10.1023_a:1022608410710. 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.