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The Dai–Liao nonlinear conjugate gradient method with optimal parameter choices

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  • Babaie-Kafaki, Saman
  • Ghanbari, Reza

Abstract

Minimizing two different upper bounds of the matrix which generates search directions of the nonlinear conjugate gradient method proposed by Dai and Liao, two modified conjugate gradient methods are proposed. Under proper conditions, it is briefly shown that the methods are globally convergent when the line search fulfills the strong Wolfe conditions. Numerical comparisons between the implementations of the proposed methods and the conjugate gradient methods proposed by Hager and Zhang, and Dai and Kou, are made on a set of unconstrained optimization test problems of the CUTEr collection. The results show the efficiency of the proposed methods in the sense of the performance profile introduced by Dolan and Moré.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:234:y:2014:i:3:p:625-630
    DOI: 10.1016/j.ejor.2013.11.012
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    References listed on IDEAS

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    2. Avinoam Perry, 1976. "A Modified Conjugate Gradient Algorithm," Discussion Papers 229, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. 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.
    4. Wenyu Sun & Ya-Xiang Yuan, 2006. "Optimization Theory and Methods," Springer Optimization and Its Applications, Springer, number 978-0-387-24976-6, June.
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    Cited by:

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    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. Branislav Ivanov & Gradimir V. Milovanović & Predrag S. Stanimirović, 2023. "Accelerated Dai-Liao projection method for solving systems of monotone nonlinear equations with application to image deblurring," Journal of Global Optimization, Springer, vol. 85(2), pages 377-420, February.
    4. Qi Tian & Xiaoliang Wang & Liping Pang & Mingkun Zhang & Fanyun Meng, 2021. "A New Hybrid Three-Term Conjugate Gradient Algorithm for Large-Scale Unconstrained Problems," Mathematics, MDPI, vol. 9(12), pages 1-13, June.
    5. 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.
    6. Zohre Aminifard & Saman Babaie-Kafaki, 2019. "An optimal parameter choice for the Dai–Liao family of conjugate gradient methods by avoiding a direction of the maximum magnification by the search direction matrix," 4OR, Springer, vol. 17(3), pages 317-330, September.
    7. Saman Babaie-Kafaki & Reza Ghanbari, 2017. "A class of adaptive Dai–Liao conjugate gradient methods based on the scaled memoryless BFGS update," 4OR, Springer, vol. 15(1), pages 85-92, March.
    8. 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.
    9. 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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