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The Modified HZ Conjugate Gradient Algorithm for Large-Scale Nonsmooth Optimization

Author

Listed:
  • Gonglin Yuan
  • Zhou Sheng
  • Wenjie Liu

Abstract

In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better efficiency for large-scale nonsmooth problems, and several problems are tested (with the maximum dimensions to 100,000 variables).

Suggested Citation

  • 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.
    • Handle: RePEc:plo:pone00:0164289
    DOI: 10.1371/journal.pone.0164289
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    References listed on IDEAS

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    1. 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.
    2. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
    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. Gonglin Yuan & Xiwen Lu, 2009. "A modified PRP conjugate gradient method," Annals of Operations Research, Springer, vol. 166(1), pages 73-90, February.
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    Cited by:

    1. 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.
    2. 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.
    3. Zhou Sheng & Gonglin Yuan, 2018. "An effective adaptive trust region algorithm for nonsmooth minimization," Computational Optimization and Applications, Springer, vol. 71(1), pages 251-271, September.

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