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An improved Dai–Kou conjugate gradient algorithm for unconstrained optimization

Author

Listed:
  • Zexian Liu

    (Xidian University
    Chinese Academy of Sciences)

  • Hongwei Liu

    (Xidian University)

  • Yu-Hong Dai

    (Chinese Academy of Sciences)

Abstract

It is gradually accepted that the loss of orthogonality of the gradients in a conjugate gradient algorithm may decelerate the convergence rate to some extent. The Dai–Kou conjugate gradient algorithm (SIAM J Optim 23(1):296–320, 2013), called CGOPT, has attracted many researchers’ attentions due to its numerical efficiency. In this paper, we present an improved Dai–Kou conjugate gradient algorithm for unconstrained optimization, which only consists of two kinds of iterations. In the improved Dai–Kou conjugate gradient algorithm, we develop a new quasi-Newton method to improve the orthogonality by solving the subproblem in the subspace and design a modified strategy for the choice of the initial stepsize for improving the numerical performance. The global convergence of the improved Dai–Kou conjugate gradient algorithm is established without the strict assumptions in the convergence analysis of other limited memory conjugate gradient methods. Some numerical results suggest that the improved Dai–Kou conjugate gradient algorithm (CGOPT (2.0)) yields a tremendous improvement over the original Dai–Kou CG algorithm (CGOPT (1.0)) and is slightly superior to the latest limited memory conjugate gradient software package CG$$\_ $$_DESCENT (6.8) developed by Hager and Zhang (SIAM J Optim 23(4):2150–2168, 2013) for the CUTEr library.

Suggested Citation

  • Zexian Liu & Hongwei Liu & Yu-Hong Dai, 2020. "An improved Dai–Kou conjugate gradient algorithm for unconstrained optimization," Computational Optimization and Applications, Springer, vol. 75(1), pages 145-167, January.
    • Handle: RePEc:spr:coopap:v:75:y:2020:i:1:d:10.1007_s10589-019-00143-4
    DOI: 10.1007/s10589-019-00143-4
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    References listed on IDEAS

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    1. Zexian Liu & Hongwei Liu, 2019. "An Efficient Gradient Method with Approximately Optimal Stepsize Based on Tensor Model for Unconstrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 608-633, May.
    2. Avinoam Perry, 1977. "A Class of Conjugate Gradient Algorithms with a Two-Step Variable Metric Memory," Discussion Papers 269, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. D. Tarzanagh & M. Peyghami, 2015. "A new regularized limited memory BFGS-type method based on modified secant conditions for unconstrained optimization problems," Journal of Global Optimization, Springer, vol. 63(4), pages 709-728, December.
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    Cited by:

    1. Abubakar, Auwal Bala & Kumam, Poom & Malik, Maulana & Ibrahim, Abdulkarim Hassan, 2022. "A hybrid conjugate gradient based approach for solving unconstrained optimization and motion control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 640-657.

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