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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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
Keywords
- Nonlinear equations
- Derivative-free method
- Projection operator
- Convergence analysis
- Numerical experiments