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A Nonlinear Conjugate Gradient Method Using Inexact First-Order Information

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Abstract

Conjugate gradient methods are widely used for solving nonlinear optimization problems. In some practical problems, we can only get approximate values of the objective function and its gradient. It is necessary to consider optimization algorithms that use inexact function evaluations and inexact gradients. In this paper, we propose an inexact nonlinear conjugate gradient (INCG) method to solve such problems. Under some mild conditions, the global convergence of INCG is proved. Specifically, we establish the linear convergence of INCG when the objective function is strongly convex. Numerical results demonstrate that, compared to the state-of-the-art algorithms, INCG is an effective method.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China NSFC-11971118. The authors are grateful to the associate editor and the two anonymous referees for their valuable comments and suggestions. Their comments and suggestions have improved the presentation of the paper significantly.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Tiantian Zhao & Wei Hong Yang

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  1. Tiantian Zhao
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  2. Wei Hong Yang
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Correspondence to Tiantian Zhao.

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Communicated by Emanuele Galligani.

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Zhao, T., Yang, W.H. A Nonlinear Conjugate Gradient Method Using Inexact First-Order Information. J Optim Theory Appl 198, 502–530 (2023). https://doi.org/10.1007/s10957-023-02243-y

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