IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v56y2013i2p317-341.html
   My bibliography  Save this article

Symmetric Perry conjugate gradient method

Author

Listed:
  • Dongyi Liu
  • Genqi Xu

Abstract

A family of new conjugate gradient methods is proposed based on Perry’s idea, which satisfies the descent property or the sufficient descent property for any line search. In addition, based on the scaling technology and the restarting strategy, a family of scaling symmetric Perry conjugate gradient methods with restarting procedures is presented. The memoryless BFGS method and the SCALCG method are the special forms of the two families of new methods, respectively. Moreover, several concrete new algorithms are suggested. Under Wolfe line searches, the global convergence of the two families of the new methods is proven by the spectral analysis for uniformly convex functions and nonconvex functions. The preliminary numerical comparisons with CG_DESCENT and SCALCG algorithms show that these new algorithms are very effective algorithms for the large-scale unconstrained optimization problems. Finally, a remark for further research is suggested. Copyright The Author(s) 2013

Suggested Citation

  • Dongyi Liu & Genqi Xu, 2013. "Symmetric Perry conjugate gradient method," Computational Optimization and Applications, Springer, vol. 56(2), pages 317-341, October.
    • Handle: RePEc:spr:coopap:v:56:y:2013:i:2:p:317-341
    DOI: 10.1007/s10589-013-9558-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-013-9558-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-013-9558-3?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. David F. Shanno, 1978. "Conjugate Gradient Methods with Inexact Searches," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 244-256, August.
    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. Yasushi Narushima & Shummin Nakayama & Masashi Takemura & Hiroshi Yabe, 2023. "Memoryless Quasi-Newton Methods Based on the Spectral-Scaling Broyden Family for Riemannian Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 639-664, May.
    2. Churlzu Lim & Hanif Sherali & Stan Uryasev, 2010. "Portfolio optimization by minimizing conditional value-at-risk via nondifferentiable optimization," Computational Optimization and Applications, Springer, vol. 46(3), pages 391-415, July.
    3. Fischer, Manfred M. & Staufer, Petra, 1998. "Optimization in an Error Backpropagation Neural Network Environment with a Performance Test on a Pattern Classification Problem," MPRA Paper 77810, University Library of Munich, Germany.
    4. B. Sellami & Y. Chaib, 2016. "A new family of globally convergent conjugate gradient methods," Annals of Operations Research, Springer, vol. 241(1), pages 497-513, June.
    5. Neculai Andrei, 2013. "Another Conjugate Gradient Algorithm with Guaranteed Descent and Conjugacy Conditions for Large-scale Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 159-182, October.
    6. Ke-Lin Du & Chi-Sing Leung & Wai Ho Mow & M. N. S. Swamy, 2022. "Perceptron: Learning, Generalization, Model Selection, Fault Tolerance, and Role in the Deep Learning Era," Mathematics, MDPI, vol. 10(24), pages 1-46, December.
    7. Shummin Nakayama & Yasushi Narushima & Hiroshi Yabe, 2021. "Inexact proximal memoryless quasi-Newton methods based on the Broyden family for minimizing composite functions," Computational Optimization and Applications, Springer, vol. 79(1), pages 127-154, May.
    8. N. Mahdavi-Amiri & M. Shaeiri, 2020. "A conjugate gradient sampling method for nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 73-90, March.
    9. Abubakar, Auwal Bala & Kumam, Poom & Malik, Maulana & Ibrahim, Abdulkarim Hassan, 2022. "A hybrid conjugate gradient based approach for solving unconstrained optimization and motion control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 640-657.
    10. Andrei, Neculai, 2010. "Accelerated scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization," European Journal of Operational Research, Elsevier, vol. 204(3), pages 410-420, August.
    11. Hanif D. Sherali & Churlzu Lim, 2007. "Enhancing Lagrangian Dual Optimization for Linear Programs by Obviating Nondifferentiability," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 3-13, February.
    12. David Ek & Anders Forsgren, 2021. "Exact linesearch limited-memory quasi-Newton methods for minimizing a quadratic function," Computational Optimization and Applications, Springer, vol. 79(3), pages 789-816, July.
    13. T. L. Jensen & M. Diehl, 2017. "An Approach for Analyzing the Global Rate of Convergence of Quasi-Newton and Truncated-Newton Methods," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 206-221, January.
    14. Chi-Cheong Chris Wong & Man-Chung Chan & Chi-Chung Lam, 2000. "Financial Time Series Forecasting By Neural Network Using Conjugate Gradient Learning Algorithm And Multiple Linear Regression Weight Initialization," Computing in Economics and Finance 2000 61, Society for Computational Economics.
    15. Hiroyuki Sakai & Hideaki Iiduka, 2024. "Modified Memoryless Spectral-Scaling Broyden Family on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 834-853, August.
    16. Saman Babaie-Kafaki, 2012. "A note on the global convergence theorem of the scaled conjugate gradient algorithms proposed by Andrei," Computational Optimization and Applications, Springer, vol. 52(2), pages 409-414, June.

    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:56:y:2013:i:2:p:317-341. 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.