Abstract
In this paper, we propose a three-term conjugate gradient method, which has two attractive properties that the search direction is descent and satisfies the famous D-L conjugacy condition without any line search. Moreover, this new three-term conjugate gradient method can be viewed as a modification of the memoryless BFGS method. By combining this new three-term conjugate gradient method with the projection technique proposed by Solodov and Svailter in 1998, we establish a three-term derivative-free projection method for solving nonlinear monotone system of equations. Due to maintain some nice properties of conjugate gradient method such as the simplicity and the low storage, the proposed projection method is very suitable to solve large-scale nonlinear monotone system of equations. The global convergence and R-linear convergence rate of the proposed projection method are proved under some appropriate conditions. The preliminary numerical results are also given to indicate that the proposed projection method is effective and robust.
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The authors declare that they have no conflict of interest. Informed consent was obtained from all individual participants included in the study.
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This research was partially supported by the National Natural Science Foundation of China (Grant number: 11171362), Specialized Research Fund for the Doctoral Program of Higher Education (Grant number: 20120191110031), and Scientific and Technological Research Program of Chongqing Municipal Education Commission (Grant number: KJ1501003).
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Liu, J.K., Li, S.J. A three-term derivative-free projection method for nonlinear monotone system of equations. Calcolo 53, 427–450 (2016). https://doi.org/10.1007/s10092-015-0156-x
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DOI: https://doi.org/10.1007/s10092-015-0156-x
Keywords
- Nonlinear monotone system of equations
- Derivative-free method
- Conjugate gradient method
- Projection method
- Global convergence