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A conjugate gradient algorithm without Lipchitz continuity and its applications

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Abstract

An improved conjugate gradient algorithm is proposed that does not rely on the line search rule and automatically achieves sufficient descent and trust region qualities. It is applicable to solve unconstrained problems and large-scale nonsmooth problems. Furthermore, it demonstrates global convergence properties without the need for Lipschitz continuity conditions. Numerical experiments on nonconvex unconstrained problems and large scale nonsmooth convex optimization problems demonstrate the effectiveness and efficiency of the proposed algorithm compared with the same structural algorithm. Finally, the new algorithm is applied to Muskingum model solving in engineering problems and image restoration, which shows the prospect of the new algorithm.

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Funding

This work is supported by Guangxi Science and Technology base and Talent Project (Grant No. AD22080047), the National Natural Science Foundation of Guangxi Province (Grant No. 2023GXNFSBA 026063), the Innovation Funds of Chinese University (Grant No. 2021BCF03001), and the special foundation for Guangxi Ba Gui Scholars.

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  1. School of Mathematics and Information Science, Center for Applied Mathematics of Guangxi (Guangxi University), Guangxi University, Nanning, 530004, Guangxi, China

    Huiyun Liu & Haishan Feng

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  1. Huiyun Liu
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  2. Haishan Feng
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Correspondence to Haishan Feng.

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Liu, H., Feng, H. A conjugate gradient algorithm without Lipchitz continuity and its applications. J. Appl. Math. Comput. (2024). https://doi.org/10.1007/s12190-024-02088-2

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  • DOI: https://doi.org/10.1007/s12190-024-02088-2

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