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A Modified Spectral Conjugate Gradient Method with Global Convergence

Author

Listed:
  • Parvaneh Faramarzi

    (Razi University)

  • Keyvan Amini

    (Razi University)

Abstract

In this paper, a modified version of the spectral conjugate gradient algorithm suggested by Jian, Chen, Jiang, Zeng and Yin is proposed. It is proved that the new method is globally convergent for general nonlinear functions, under some standard assumptions. Based on the modified secant condition and quasi-Newton directions, some new spectral parameters are introduced. It is shown that the search direction satisfies the sufficient descent property independent of the line search. Numerical experiments indicate a promising behavior of the new algorithm, especially for large-scale problems.

Suggested Citation

  • Parvaneh Faramarzi & Keyvan Amini, 2019. "A Modified Spectral Conjugate Gradient Method with Global Convergence," Journal of Optimization Theory and Applications, Springer, vol. 182(2), pages 667-690, August.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:2:d:10.1007_s10957-019-01527-6
    DOI: 10.1007/s10957-019-01527-6
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    References listed on IDEAS

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    1. Yutao Zheng & Bing Zheng, 2017. "Two New Dai–Liao-Type Conjugate Gradient Methods for Unconstrained Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 502-509, November.
    2. Avinoam Perry, 1978. "Technical Note—A Modified Conjugate Gradient Algorithm," Operations Research, INFORMS, vol. 26(6), pages 1073-1078, December.
    3. 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.
    4. 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.
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    Cited by:

    1. Parvaneh Faramarzi & Keyvan Amini, 2021. "A spectral three-term Hestenes–Stiefel conjugate gradient method," 4OR, Springer, vol. 19(1), pages 71-92, March.
    2. 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.
    3. Qing-Rui He & Chun-Rong Chen & Sheng-Jie Li, 2023. "Spectral conjugate gradient methods for vector optimization problems," Computational Optimization and Applications, Springer, vol. 86(2), pages 457-489, November.

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