IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v22y2024i2d10.1007_s10288-023-00544-6.html
   My bibliography  Save this article

A new self-scaling memoryless quasi-Newton update for unconstrained optimization

Author

Listed:
  • M. Jourak

    (Payame Noor University)

  • S. Nezhadhosein

    (Payame Noor University)

  • F. Rahpeymaii

    (Technical and Vocational University (TVU))

Abstract

Based on the augmented version of the quasi-Newton method proposed by Aminifard et al. (App. Num. Math. 167:187–201, 2021), a new scaled parameter of the self-scaling memoryless BFGS update formula is proposed. The idea is to cluster the eigenvalues of the search direction matrix, obtained by minimizing the difference between the largest and the smallest eigenvalues of the matrix. The sufficient descent property is proved for uniformly convex functions, and the global convergence of the proposed algorithm is proved both for the uniformly convex and general nonlinear objective functions. Numerical experiments on a set of test functions of the CUTEr collection show that the proposed method is efficient. In addition, the proposed algorithm is effectively applied to salt and pepper noise elimination problem.

Suggested Citation

  • M. Jourak & S. Nezhadhosein & F. Rahpeymaii, 2024. "A new self-scaling memoryless quasi-Newton update for unconstrained optimization," 4OR, Springer, vol. 22(2), pages 235-252, June.
    • Handle: RePEc:spr:aqjoor:v:22:y:2024:i:2:d:10.1007_s10288-023-00544-6
    DOI: 10.1007/s10288-023-00544-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-023-00544-6
    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/s10288-023-00544-6?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. J. Z. Zhang & N. Y. Deng & L. H. Chen, 1999. "New Quasi-Newton Equation and Related Methods for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 147-167, July.
    2. Kaori Sugiki & Yasushi Narushima & Hiroshi Yabe, 2012. "Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 733-757, June.
    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. Babaie-Kafaki, Saman & Ghanbari, Reza, 2014. "The Dai–Liao nonlinear conjugate gradient method with optimal parameter choices," European Journal of Operational Research, Elsevier, vol. 234(3), pages 625-630.
    2. 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.
    3. 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.
    4. Yu, Yang & Wang, Yu & Deng, Rui & Yin, Yu, 2023. "New DY-HS hybrid conjugate gradient algorithm for solving optimization problem of unsteady partial differential equations with convection term," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 677-701.
    5. Mina Torabi & Mohammad-Mehdi Hosseini, 2018. "A New Descent Algorithm Using the Three-Step Discretization Method for Solving Unconstrained Optimization Problems," Mathematics, MDPI, vol. 6(4), pages 1-18, April.
    6. Yong Li & Gonglin Yuan & Zhou Sheng, 2018. "An active-set algorithm for solving large-scale nonsmooth optimization models with box constraints," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-16, January.
    7. XiaoLiang Dong & Deren Han & Zhifeng Dai & Lixiang Li & Jianguang Zhu, 2018. "An Accelerated Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 944-961, December.
    8. Auwal Bala Abubakar & Poom Kumam & Aliyu Muhammed Awwal & Phatiphat Thounthong, 2019. "A Modified Self-Adaptive Conjugate Gradient Method for Solving Convex Constrained Monotone Nonlinear Equations for Signal Recovery Problems," Mathematics, MDPI, vol. 7(8), pages 1-24, August.
    9. Saman Babaie-Kafaki & Reza Ghanbari, 2016. "Descent Symmetrization of the Dai–Liao Conjugate Gradient Method," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(02), pages 1-10, April.
    10. Dong, Xiao Liang & Liu, Hong Wei & He, Yu Bo, 2015. "New version of the three-term conjugate gradient method based on spectral scaling conjugacy condition that generates descent search direction," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 606-617.
    11. Gonglin Yuan & Xiaoliang Wang & Zhou Sheng, 2020. "The Projection Technique for Two Open Problems of Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 590-619, August.
    12. Mehiddin Al-Baali & Humaid Khalfan, 2012. "A combined class of self-scaling and modified quasi-Newton methods," Computational Optimization and Applications, Springer, vol. 52(2), pages 393-408, June.
    13. Bakhtawar Baluch & Zabidin Salleh & Ahmad Alhawarat & U. A. M. Roslan, 2017. "A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence," Journal of Mathematics, Hindawi, vol. 2017, pages 1-12, September.
    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. Waziri, Mohammed Yusuf & Ahmed, Kabiru & Sabi’u, Jamilu, 2019. "A family of Hager–Zhang conjugate gradient methods for system of monotone nonlinear equations," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 645-660.
    16. D. Tarzanagh & M. Peyghami, 2015. "A new regularized limited memory BFGS-type method based on modified secant conditions for unconstrained optimization problems," Journal of Global Optimization, Springer, vol. 63(4), pages 709-728, December.
    17. 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.
    18. Zexian Liu & Hongwei Liu, 2019. "An Efficient Gradient Method with Approximately Optimal Stepsize Based on Tensor Model for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 608-633, May.
    19. 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.
    20. 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.

    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:2:d:10.1007_s10288-023-00544-6. 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.