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An Accelerated Three-Term Conjugate Gradient Method with Sufficient Descent Condition and Conjugacy Condition

Author

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  • XiaoLiang Dong

    (North Minzu University)

  • Deren Han

    (Beihang University)

  • Zhifeng Dai

    (Changsha University of Science and Technology)

  • Lixiang Li

    (Guilin University of Electronic Technology)

  • Jianguang Zhu

    (Shandong University of Science and Technology)

Abstract

An accelerated three-term conjugate gradient method is proposed, in which the search direction can satisfy the sufficient descent condition as well as extended Dai–Liao conjugacy condition. Different from the existent methods, a dynamical compensation strategy in our proposed method is considered, that is Li–Fushikuma-type quasi-Newton equation is satisfied as much as possible, otherwise, to some extent, the singular values of iteration matrix of search directions will adaptively clustered, which substantially benefits acceleration the convergence or reduction in the condition number of iteration matrix. Global convergence is established under mild conditions for general objective functions. We also report some numerical results to show its efficiency.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:3:d:10.1007_s10957-018-1377-3
    DOI: 10.1007/s10957-018-1377-3
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    References listed on IDEAS

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    10. 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.
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    13. 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.
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    3. Zhu, Zhibin & Zhang, Dongdong & Wang, Shuo, 2020. "Two modified DY conjugate gradient methods for unconstrained optimization problems," Applied Mathematics and Computation, Elsevier, vol. 373(C).

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