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Received March 9, 2021; Accepted September 5, 2021; Published September 29, 2021
Abstract. We propose a derivative-free cubic regularization method for solving nonlinear systems of equations without available derivatives. The novel feature of the method is that, based on locally interpolation models, the search direction in each iteration is allowed to be a solution of a model-based cubic regularization approximation formulated by the special structure of equations that ensures a significant improvement. We present a set of wild conditions that the search direction must be satisfied so that the global convergence of the method for solving the nonlinear equations is guaranteed. The global convergence and the fast local convergence rate of the proposed method are established, and numerical experiments are provided to illustrate the reliability of the proposed method.
How to Cite this Article:
Xiaojin Huang, A derivative-free cubic regularization method for nonlinear systems of equations, Journal of Nonlinear Functional Analysis, Vol. 2021 (2021), Article ID 28, pp. 1-22.