IDEAS home Printed from https://ideas.repec.org/a/spr/aqjoor/v18y2020i2d10.1007_s10288-019-00412-2.html
   My bibliography  Save this article

Global convergence of a family of modified BFGS methods under a modified weak-Wolfe–Powell line search for nonconvex functions

Author

Listed:
  • S. Bojari

    (Tarbiat Modares University)

  • M. R. Eslahchi

    (Tarbiat Modares University)

Abstract

In this paper, we consider an unconstrained optimization problem and propose a new family of modified BFGS methods to solve it. As it is known, classic BFGS method is not always globally convergence for nonconvex functions. To overcome this difficulty, we introduce a new modified weak-Wolfe–Powell line search technique. Under this new technique, we prove global convergence of the new family of modified BFGS methods and the classic BFGS method, for nonconvex functions. Furthermore, all members of this family have at least $$o(\Vert s \Vert ^{5})$$o(‖s‖5) error order. Our obtained results from numerical experiments on 77 standard unconstrained problems, indicate that the algorithms developed in this paper are promising and more effective than some similar algorithms.

Suggested Citation

  • S. Bojari & M. R. Eslahchi, 2020. "Global convergence of a family of modified BFGS methods under a modified weak-Wolfe–Powell line search for nonconvex functions," 4OR, Springer, vol. 18(2), pages 219-244, June.
    • Handle: RePEc:spr:aqjoor:v:18:y:2020:i:2:d:10.1007_s10288-019-00412-2
    DOI: 10.1007/s10288-019-00412-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10288-019-00412-2
    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/s10288-019-00412-2?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. Liying Liu & Shengwei Yao & Zengxin Wei, 2014. "A Modified Non-Monotone BFGS Method for Non-Convex Unconstrained Optimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-15.
    2. 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.
    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. Mehiddin Al-Baali & Lucio Grandinetti & Ornella Pisacane, 2014. "Damped Techniques for the Limited Memory BFGS Method for Large-Scale Optimization," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 688-699, May.
    5. 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.
    6. Gonglin Yuan & Zengxin Wei, 2010. "Convergence analysis of a modified BFGS method on convex minimizations," Computational Optimization and Applications, Springer, vol. 47(2), pages 237-255, October.
    7. 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.
    8. 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.
    9. Hao Liu & Hai-Jun Wang & Xiao-Yan Qian & Qing-Sheng Shi, 2013. "A Class Of Modified Bfgs Methods With Function Value Information For Unconstrained Optimization," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(06), pages 1-20.
    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. 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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Parvaneh Faramarzi & Keyvan Amini, 2021. "A spectral three-term Hestenes–Stiefel conjugate gradient method," 4OR, Springer, vol. 19(1), pages 71-92, March.
    8. 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.
    9. 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.
    10. 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.
    11. Hassan Mohammad & Mohammed Yusuf Waziri, 2019. "Structured Two-Point Stepsize Gradient Methods for Nonlinear Least Squares," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 298-317, April.
    12. Fahimeh Biglari & Maghsud Solimanpur, 2013. "Scaling on the Spectral Gradient Method," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 626-635, August.
    13. Qi Tian & Xiaoliang Wang & Liping Pang & Mingkun Zhang & Fanyun Meng, 2021. "A New Hybrid Three-Term Conjugate Gradient Algorithm for Large-Scale Unconstrained Problems," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    14. Mehiddin Al-Baali & Andrea Caliciotti & Giovanni Fasano & Massimo Roma, 2017. "Exploiting damped techniques for nonlinear conjugate gradient methods," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(3), pages 501-522, December.
    15. Gonglin Yuan & Zhou Sheng & Wenjie Liu, 2016. "The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-15, October.
    16. Gonglin Yuan & Xiabin Duan & Wenjie Liu & Xiaoliang Wang & Zengru Cui & Zhou Sheng, 2015. "Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-24, October.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    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:18:y:2020:i:2:d:10.1007_s10288-019-00412-2. 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.