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A Modified Nonlinear Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization

Author

Listed:
  • Tsegay Giday Woldu

    (Beijing University of Technology)

  • Haibin Zhang

    (Beijing University of Technology)

  • Xin Zhang

    (Chinese Academy of Science)

  • Yemane Hailu Fissuh

    (Beijing University of Technology)

Abstract

Nonlinear conjugate gradient methods are among the most preferable and effortless methods to solve smooth optimization problems. Due to their clarity and low memory requirements, they are more desirable for solving large-scale smooth problems. Conjugate gradient methods make use of gradient and the previous direction information to determine the next search direction, and they require no numerical linear algebra. However, the utility of nonlinear conjugate gradient methods has not been widely employed in solving nonsmooth optimization problems. In this paper, a modified nonlinear conjugate gradient method, which achieves the global convergence property and numerical efficiency, is proposed to solve large-scale nonsmooth convex problems. The new method owns the search direction, which generates sufficient descent property and belongs to a trust region. Under some suitable conditions, the global convergence of the proposed algorithm is analyzed for nonsmooth convex problems. The numerical efficiency of the proposed algorithm is tested and compared with some existing methods on some large-scale nonsmooth academic test problems. The numerical results show that the new algorithm has a very good performance in solving large-scale nonsmooth problems.

Suggested Citation

  • Tsegay Giday Woldu & Haibin Zhang & Xin Zhang & Yemane Hailu Fissuh, 2020. "A Modified Nonlinear Conjugate Gradient Algorithm for Large-Scale Nonsmooth Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 223-238, April.
    • Handle: RePEc:spr:joptap:v:185:y:2020:i:1:d:10.1007_s10957-020-01636-7
    DOI: 10.1007/s10957-020-01636-7
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    References listed on IDEAS

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    1. J. R. Birge & L. Qi & Z. Wei, 1998. "Convergence Analysis of Some Methods for Minimizing a Nonsmooth Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 97(2), pages 357-383, May.
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    4. 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.
    5. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    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.
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    Cited by:

    1. Luyun Wang & Bo Zhou, 2023. "A Modified Gradient Method for Distributionally Robust Logistic Regression over the Wasserstein Ball," Mathematics, MDPI, vol. 11(11), pages 1-15, May.

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