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A Self-Adjusting Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

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  • XiaoLiang Dong

    (Xidian University)

  • Hongwei Liu

    (Xidian University)

  • Yubo He

    (Huaihua University)

Abstract

In this paper, a self-adjust conjugate gradient method is proposed for solving unconstrained problems, which can generate sufficient descent directions at each iteration. Different from the existent methods, a dynamical adjustment of conjugacy condition in our proposed method is developed, which can be regarded as the inheritance and development of properties of standard Hestenes–Stiefel method. Under mild condition, we show the proposed method convergent globally even if the objective function is nonconvex. Numerical results illustrate that our method can efficiently solve the test problems and therefore is promising.

Suggested Citation

  • XiaoLiang Dong & Hongwei Liu & Yubo He, 2015. "A Self-Adjusting Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 225-241, April.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:1:d:10.1007_s10957-014-0601-z
    DOI: 10.1007/s10957-014-0601-z
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    References listed on IDEAS

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    1. Wanyou Cheng & Donghui Li, 2012. "An Active Set Modified Polak–Ribiére–Polyak Method for Large-Scale Nonlinear Bound Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 1084-1094, December.
    2. Neculai Andrei, 2013. "Another Conjugate Gradient Algorithm with Guaranteed Descent and Conjugacy Conditions for Large-scale Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 159(1), pages 159-182, October.
    3. Xiao-Min An & Dong-Hui Li & Yunhai Xiao, 2011. "Sufficient descent directions in unconstrained optimization," Computational Optimization and Applications, Springer, vol. 48(3), pages 515-532, April.
    4. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, July.
    5. 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.
    6. Songhai Deng & Zhong Wan & Xiaohong Chen, 2013. "An Improved Spectral Conjugate Gradient Algorithm for Nonconvex Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 820-842, June.
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    Cited by:

    1. XiaoLiang Dong & Deren Han & Zhifeng Dai & Lixiang Li & Jianguang Zhu, 2018. "An Accelerated Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition," Journal of Optimization Theory and Applications, Springer, vol. 179(3), pages 944-961, December.
    2. Hongwei Liu & Zexian Liu, 2019. "An Efficient Barzilai–Borwein Conjugate Gradient Method for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 879-906, March.
    3. Jose Giovany Babativa-Márquez & José Luis Vicente-Villardón, 2021. "Logistic Biplot by Conjugate Gradient Algorithms and Iterated SVD," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
    4. Gao, Peiting & He, Chuanjiang & Liu, Yang, 2019. "An adaptive family of projection methods for constrained monotone nonlinear equations with applications," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 1-16.
    5. Dong, Xiao Liang & Liu, Hong Wei & He, Yu Bo, 2015. "New version of the three-term conjugate gradient method based on spectral scaling conjugacy condition that generates descent search direction," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 606-617.
    6. Xiaoyu Wu & Hu Shao & Pengjie Liu & Yue Zhuo, 2023. "An Inertial Spectral CG Projection Method Based on the Memoryless BFGS Update," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1130-1155, September.
    7. Zhifeng Dai, 2017. "Comments on Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 175(1), pages 286-291, October.

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