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Some New Descent Nonlinear Conjugate Gradient Methods for Unconstrained Optimization Problems with Global Convergence

Author

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  • Min Li

    (College of Mathematics, Hunan University, Changsha, Hunan, P. R. China2Department of Mathematics and Computational Science, Huaihua University, Huaihua, Hunan, P. R. China)

Abstract

In this paper, we develop some three term nonlinear conjugate gradient methods based on the Hestenes–Stiefel (HS), the Polak–Ribière–Polyak (PRP) and the Liu–Storey (LS) methods. The proposed algorithms always generate sufficient descent directions which satisfy gkTd k = −∥gk∥2. When the Wolfe or the Armijo line search is used, we establish the global convergence of the proposed methods in a concise way. Moreover, the linear convergence rate of the methods is discussed as well. The extensive numerical results show the efficiency of the proposed methods.

Suggested Citation

  • Min Li, 2024. "Some New Descent Nonlinear Conjugate Gradient Methods for Unconstrained Optimization Problems with Global Convergence," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 41(02), pages 1-17, April.
    • Handle: RePEc:wsi:apjorx:v:41:y:2024:i:02:n:s0217595923500203
    DOI: 10.1142/S0217595923500203
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