IDEAS home Printed from https://ideas.repec.org/a/spr/jglopt/v63y2015i4p709-728.html
   My bibliography  Save this article

A new regularized limited memory BFGS-type method based on modified secant conditions for unconstrained optimization problems

Author

Listed:
  • D. Tarzanagh
  • M. Peyghami

Abstract

In the framework of large-scale optimization problems, the standard BFGS method is not affordable due to memory constraints. The so-called limited-memory BFGS (L-BFGS) method is an adaption of the BFGS method for large-scale settings. However, the standard BFGS method and therefore the standard L-BFGS method only use the gradient information of the objective function and neglect function values. In this paper, we propose a new regularized L-BFGS method for solving large scale unconstrained optimization problems in which more available information from the function and gradient values are employed to approximate the curvature of the objective function. The proposed method utilizes a class of modified quasi-Newton equations in order to achieve higher order accuracy in approximating the second order curvature of the objective function. Under some standard assumptions, we provide the global convergence property of the new method. In order to provide an efficient method for finding global minima of a continuously differentiable function, a hybrid algorithm that combines a genetic algorithm (GA) with the new proposed regularized L-BFGS method has been proposed. This combination leads the iterates to a stationary point of the objective function with higher chance of being global minima. Numerical results show the efficiency and robustness of the new proposed regularized L-BFGS and its hybridized version with GA in practice. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:63:y:2015:i:4:p:709-728
    DOI: 10.1007/s10898-015-0310-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10898-015-0310-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10898-015-0310-7?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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Zexian Liu & Hongwei Liu & Yu-Hong Dai, 2020. "An improved Dai–Kou conjugate gradient algorithm for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 75(1), pages 145-167, January.

    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. Zhanwen Shi & Guanyu Yang & Yunhai Xiao, 2016. "A limited memory BFGS algorithm for non-convex minimization with applications in matrix largest eigenvalue problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(2), pages 243-264, April.
    18. Vahid Morovati & Hadi Basirzadeh & Latif Pourkarimi, 2018. "Quasi-Newton methods for multiobjective optimization problems," 4OR, Springer, vol. 16(3), pages 261-294, September.
    19. 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.
    20. Yueting, Yang & Chengxian, Xu, 2007. "A compact limited memory method for large scale unconstrained optimization," European Journal of Operational Research, Elsevier, vol. 180(1), pages 48-56, 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:jglopt:v:63:y:2015:i:4:p:709-728. 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.