Abstract
Based on a modified line search scheme, this paper presents a new derivative-free projection method for solving nonlinear monotone equations with convex constraints, which can be regarded as an extension of the scaled conjugate gradient method and the projection method. Under appropriate conditions, the global convergence and linear convergence rate of the proposed method is proven. Preliminary numerical results are also reported to show that this method is promising.
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Acknowledgments
The authors would like to thank the anonymous referees and the editor for their patience and valuable comments and suggestions that greatly improved this paper. This work is partially supported by NNSF of China (No. 11261015) and NSF of Hainan Province (No. 2016CXTD004, No. 111001).
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Ou, Y., Li, J. A new derivative-free SCG-type projection method for nonlinear monotone equations with convex constraints. J. Appl. Math. Comput. 56, 195–216 (2018). https://doi.org/10.1007/s12190-016-1068-x
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DOI: https://doi.org/10.1007/s12190-016-1068-x
Keywords
- Nonlinear monotone equations
- Scaled conjugate gradient method
- Derivative-free method
- Projection method
- Convergence analysis