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A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations

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Abstract

In this paper, we propose a general framework that provides a unified convergence analysis of the derivative-free projection-based method (DFPM) for solving large-scale constrained nonlinear monotone equations. The new results provide a complete picture on the convergence guarantees of DFPM and cover the existing relevant convergence results as special cases. Preliminary numerical experiment results are also reported to show the numerical performance of six line search schemes used in the existing DFPM.

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Acknowledgements

The authors would like to thank the anonymous referees and the associate editor for their careful reading of our manuscript and their valuable comments and constructive suggestions that greatly improved this manuscript’s quality.

Funding

This work is supported by NNSF of China (Nos.11961018, 12261028), STSF of Hainan Province (No. ZDYF2021SHFZ231), and Innovative Project for Postgraduates of Hainan Province (No. Qhys2021-207).

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Authors and Affiliations

  1. Department of Mathematics, Hainan University, Haikou, 570228, Hainan, China

    Yigui Ou & Lin Li

  2. Key Laboratory of Engineering Modeling and Statistical Computation of Hainan Province, Haikou, 570228, Hainan, China

    Yigui Ou

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  1. Yigui Ou
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  2. Lin Li
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Correspondence to Yigui Ou.

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Ou, Y., Li, L. A unified convergence analysis of the derivative-free projection-based method for constrained nonlinear monotone equations. Numer Algor 93, 1639–1660 (2023). https://doi.org/10.1007/s11075-022-01483-9

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  • DOI: https://doi.org/10.1007/s11075-022-01483-9

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