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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
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    References listed on IDEAS

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    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.
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    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
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