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A class of three-term derivative-free methods for large-scale nonlinear monotone system of equations and applications to image restoration problems

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Abstract

In this paper, we develop a class of derivative-free methods for large-scale nonlinear monotone system of equations. They combine the hybrid three-term conjugate gradient method, which are designed for unconstrained problems and always satisfy the Dai-Liao conjugate condition and the sufficient descent property, and the projection technique proposed by Solodov and Svaiter in 1998. Under some mild conditions, the proposed methods are globally convergent and own R-linear convergence rate. Nine testing problems with 15 large dimensions varying from 1000 to 900000 are referred. Numerical results indicate that the proposed algorithms are more efficient and reliable than the other methods for the testing problems. At last, we also apply the proposed method to some image restoration problems and the results also show that the proposed method is effective and promising.

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Authors and Affiliations

  1. Department of Mathematics Science, School of Science, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Xiaoliang Wang

  2. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Yuzhu Tian & Liping Pang

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  1. Xiaoliang Wang
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  2. Yuzhu Tian
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  3. Liping Pang
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Correspondence to Xiaoliang Wang.

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This work is supported by Science Foundation of Zhejiang Sci-Tech University (ZSTU) under Grant No. 21062347-Y.

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Wang, X., Tian, Y. & Pang, L. A class of three-term derivative-free methods for large-scale nonlinear monotone system of equations and applications to image restoration problems. J. Appl. Math. Comput. 69, 1269–1296 (2023). https://doi.org/10.1007/s12190-022-01790-3

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