scholarly journals On the Quadratic Convergence of the Cubic Regularization Method under a Local Error Bound Condition

2019 ◽  
Vol 29 (1) ◽  
pp. 904-932 ◽  
Author(s):  
Man-Chung Yue ◽  
Zirui Zhou ◽  
Anthony Man-Cho So
Keyword(s):  
Error Bound ◽  
Regularization Method ◽  
Quadratic Convergence ◽  
Local Error ◽  
Local Error Bound ◽  
Cubic Regularization ◽  
Local Error Bound Condition

scholarly journals A New Modified Efficient Levenberg–Marquardt Method for Solving Systems of Nonlinear Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Zhenxiang Wu ◽  
Tong Zhou ◽  
Lei Li ◽  
Liang Chen ◽  
Yanfang Ma
Keyword(s):  
Error Bound ◽  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Systems Of Nonlinear Equations ◽  
Local Error ◽  
Local Error Bound ◽  
Marquardt Method ◽  
Marquardt Algorithm ◽  
Levenberg Marquardt ◽  
Local Error Bound Condition

For systems of nonlinear equations, a modified efficient Levenberg–Marquardt method with new LM parameters was developed by Amini et al. (2018). The convergence of the method was proved under the local error bound condition. In order to enhance this method, using nonmonotone technique, we propose a new Levenberg–Marquardt parameter in this paper. The convergence of the new Levenberg–Marquardt method is shown to be at least superlinear, and numerical experiments show that the new Levenberg–Marquardt algorithm can solve systems of nonlinear equations effectively.

scholarly journals Error Bound for Conic Inequality in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jiangxing Zhu ◽  
Qinghai He ◽  
Jinchuan Lin
Keyword(s):  
Hilbert Space ◽  
Error Bound ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Local Error ◽  
Local Error Bound ◽  
Local Error Bounds ◽  
Space Case ◽  
Vector Valued Functions ◽  
Vector Valued

We consider error bound issue for conic inequalities in Hilbert spaces. In terms of proximal subdifferentials of vector-valued functions, we provide sufficient conditions for the existence of a local error bound for a conic inequality. In the Hilbert space case, our result improves and extends some existing results on local error bounds.

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