IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0120993.html
   My bibliography  Save this article

A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations

Author

Listed:
  • Yong Li
  • Gonglin Yuan
  • Zengxin Wei

Abstract

In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that the method is competitive with the norm method.

Suggested Citation

  • Yong Li & Gonglin Yuan & Zengxin Wei, 2015. "A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-13, May.
  • Handle: RePEc:plo:pone00:0120993
    DOI: 10.1371/journal.pone.0120993
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0120993
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0120993&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0120993?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
    ---><---

    References listed on IDEAS

    as
    1. Ju-liang Zhang & Yong Wang, 2003. "A new trust region method for nonlinear equations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 283-298, November.
    2. Gonglin Yuan & Xiwen Lu, 2009. "A modified PRP conjugate gradient method," Annals of Operations Research, Springer, vol. 166(1), pages 73-90, February.
    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. 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.
    2. Gonglin Yuan & Zehong Meng & Yong Li, 2016. "A Modified Hestenes and Stiefel Conjugate Gradient Algorithm for Large-Scale Nonsmooth Minimizations and Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 168(1), pages 129-152, January.
    3. Geovani Nunes Grapiglia & Jinyun Yuan & Ya-xiang Yuan, 2016. "Nonlinear Stepsize Control Algorithms: Complexity Bounds for First- and Second-Order Optimality," Journal of Optimization Theory and Applications, Springer, vol. 171(3), pages 980-997, December.
    4. Kin Keung Lai & Shashi Kant Mishra & Bhagwat Ram & Ravina Sharma, 2023. "A Conjugate Gradient Method: Quantum Spectral Polak–Ribiére–Polyak Approach for Unconstrained Optimization Problems," Mathematics, MDPI, vol. 11(23), pages 1-14, December.
    5. 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.
    6. Gonglin Yuan & Zengxin Wei & Zhongxing Wang, 2013. "Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization," Computational Optimization and Applications, Springer, vol. 54(1), pages 45-64, January.
    7. Naoki Marumo & Takayuki Okuno & Akiko Takeda, 2023. "Majorization-minimization-based Levenberg–Marquardt method for constrained nonlinear least squares," Computational Optimization and Applications, Springer, vol. 84(3), pages 833-874, April.
    8. Hamid Esmaeili & Morteza Kimiaei, 2016. "A trust-region method with improved adaptive radius for systems of nonlinear equations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 109-125, February.
    9. Morteza Kimiaei & Farzad Rahpeymaii, 2019. "A new nonmonotone line-search trust-region approach for nonlinear systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 199-232, July.
    10. 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.
    11. Keyvan Amini & Mushtak A. K. Shiker & Morteza Kimiaei, 2016. "A line search trust-region algorithm with nonmonotone adaptive radius for a system of nonlinear equations," 4OR, Springer, vol. 14(2), pages 133-152, June.
    12. Hamid Esmaeili & Morteza Kimiaei, 2016. "A trust-region method with improved adaptive radius for systems of nonlinear equations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 109-125, February.
    13. Xianfeng Ding & Quan Qu & Xinyi Wang, 2021. "A modified filter nonmonotone adaptive retrospective trust region method," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-16, June.
    14. S. Bellavia & B. Morini & E. Riccietti, 2016. "On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation," Computational Optimization and Applications, Springer, vol. 64(1), pages 1-30, May.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0120993. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.