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A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization

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  • Mehiddin Al-Baali
  • Yasushi Narushima
  • Hiroshi Yabe

Abstract

Recently, conjugate gradient methods, which usually generate descent search directions, are useful for large-scale optimization. Narushima et al. (SIAM J Optim 21:212–230, 2011 ) have proposed a three-term conjugate gradient method which satisfies a sufficient descent condition. We extend this method to two parameters family of three-term conjugate gradient methods which can be used to control the magnitude of the directional derivative. We show that these methods converge globally and work well for suitable choices of the parameters. Numerical results are also presented. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Mehiddin Al-Baali & Yasushi Narushima & Hiroshi Yabe, 2015. "A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 60(1), pages 89-110, January.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:1:p:89-110
    DOI: 10.1007/s10589-014-9662-z
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    References listed on IDEAS

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    1. Kaori Sugiki & Yasushi Narushima & Hiroshi Yabe, 2012. "Globally Convergent Three-Term Conjugate Gradient Methods that Use Secant Conditions and Generate Descent Search Directions for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 733-757, June.
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    Cited by:

    1. Bakhtawar Baluch & Zabidin Salleh & Ahmad Alhawarat & U. A. M. Roslan, 2017. "A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence," Journal of Mathematics, Hindawi, vol. 2017, pages 1-12, September.
    2. 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.
    3. Yasushi Narushima & Shummin Nakayama & Masashi Takemura & Hiroshi Yabe, 2023. "Memoryless Quasi-Newton Methods Based on the Spectral-Scaling Broyden Family for Riemannian Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 639-664, May.
    4. Auwal Bala Abubakar & Poom Kumam & Aliyu Muhammed Awwal & Phatiphat Thounthong, 2019. "A Modified Self-Adaptive Conjugate Gradient Method for Solving Convex Constrained Monotone Nonlinear Equations for Signal Recovery Problems," Mathematics, MDPI, vol. 7(8), pages 1-24, August.

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