IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v241y2016i1d10.1007_s10479-016-2120-9.html
   My bibliography  Save this article

A new family of globally convergent conjugate gradient methods

Author

Listed:
  • B. Sellami

    (Mohamed Chrif Messaadia University)

  • Y. Chaib

    (Mohamed Chrif Messaadia University)

Abstract

Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, a new family of conjugate gradient method is proposed for unconstrained optimization. This method includes the already existing two practical nonlinear conjugate gradient methods, which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the Wolfe conditions. The numerical experiments are done to test the efficiency of the new method, which implies the new method is promising. In addition the methods related to this family are uniformly discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:241:y:2016:i:1:d:10.1007_s10479-016-2120-9
    DOI: 10.1007/s10479-016-2120-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-016-2120-9
    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/s10479-016-2120-9?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.

    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.
    2. Y.H. Dai & Y. Yuan, 2001. "An Efficient Hybrid Conjugate Gradient Method for Unconstrained Optimization," Annals of Operations Research, Springer, vol. 103(1), pages 33-47, March.
    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. 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.
    2. 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.
    3. 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.
    4. Elena Tovbis & Vladimir Krutikov & Predrag Stanimirović & Vladimir Meshechkin & Aleksey Popov & Lev Kazakovtsev, 2023. "A Family of Multi-Step Subgradient Minimization Methods," Mathematics, MDPI, vol. 11(10), pages 1-24, May.
    5. Hiroyuki Sakai & Hideaki Iiduka, 2020. "Hybrid Riemannian conjugate gradient methods with global convergence properties," Computational Optimization and Applications, Springer, vol. 77(3), pages 811-830, December.
    6. Serge Gratton & Vincent Malmedy & Philippe Toint, 2012. "Using approximate secant equations in limited memory methods for multilevel unconstrained optimization," Computational Optimization and Applications, Springer, vol. 51(3), pages 967-979, April.
    7. 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.
    8. N. Andrei, 2009. "Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 249-264, May.
    9. Jose Giovany Babativa-Márquez & José Luis Vicente-Villardón, 2021. "Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    10. 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.
    11. Nash, John C. & Varadhan, Ravi, 2011. "Unifying Optimization Algorithms to Aid Software System Users: optimx for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i09).
    12. Jinbao Jian & Lin Yang & Xianzhen Jiang & Pengjie Liu & Meixing Liu, 2020. "A Spectral Conjugate Gradient Method with Descent Property," Mathematics, MDPI, vol. 8(2), pages 1-13, February.
    13. N. Mahdavi-Amiri & M. Shaeiri, 2020. "A conjugate gradient sampling method for nonsmooth optimization," 4OR, Springer, vol. 18(1), pages 73-90, March.
    14. 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.
    15. 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.
    16. Khalid Abdulaziz Alnowibet & Salem Mahdi & Ahmad M. Alshamrani & Karam M. Sallam & Ali Wagdy Mohamed, 2022. "A Family of Hybrid Stochastic Conjugate Gradient Algorithms for Local and Global Minimization Problems," Mathematics, MDPI, vol. 10(19), pages 1-37, October.
    17. Predrag S. Stanimirović & Branislav Ivanov & Snežana Djordjević & Ivona Brajević, 2018. "New Hybrid Conjugate Gradient and Broyden–Fletcher–Goldfarb–Shanno Conjugate Gradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 860-884, September.
    18. 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.
    19. 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.
    20. Saman Babaie-Kafaki, 2012. "A Quadratic Hybridization of Polak–Ribière–Polyak and Fletcher–Reeves Conjugate Gradient Methods," Journal of Optimization Theory and Applications, Springer, vol. 154(3), pages 916-932, September.

    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:annopr:v:241:y:2016:i:1:d:10.1007_s10479-016-2120-9. 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.

    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.