Convergence Rate of The Trust Region Method for Nonlinear Equations Under Local Error Bound Condition

2006 ◽  
Vol 34 (2) ◽  
pp. 215-227 ◽  
Author(s):  
Jinyan Fan
Keyword(s):  
Convergence Rate ◽  
Error Bound ◽  
Nonlinear Equations ◽  
Trust Region Method ◽  
Trust Region ◽  
Local Error ◽  
Local Error Bound ◽  
Region Method ◽  
Local Error Bound Condition

scholarly journals On convergence properties of the modified trust region method under Hölderian error bound condition

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jirui Ma ◽  
Jinyan Fan
Keyword(s):  
Error Bound ◽  
Nonlinear Equations ◽  
Trust Region Method ◽  
Trust Region ◽  
Convergence Order ◽  
Convergence Properties ◽  
Region Method

<p style='text-indent:20px;'>Trust region method is one of the important methods for nonlinear equations. In this paper, we show that the modified trust region method converges globally under the Hölderian continuity of the Jacobian. The convergence order of the method is also given under the Hölderian error bound condition.</p>

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.

A BFGS trust-region method for nonlinear equations

Computing ◽  
2011 ◽  
Vol 92 (4) ◽  
pp. 317-333 ◽  
Author(s):  
Gonglin Yuan ◽  
Zengxin Wei ◽  
Xiwen Lu
Keyword(s):  
Nonlinear Equations ◽  
Trust Region Method ◽  
Trust Region ◽  
Region Method

scholarly journals Convergence Rate Analysis of a Stochastic Trust-Region Method via Supermartingales

2019 ◽  
Vol 1 (2) ◽  
pp. 92-119 ◽  
Author(s):  
Jose Blanchet ◽  
Coralia Cartis ◽  
Matt Menickelly ◽  
Katya Scheinberg
Keyword(s):  
Convergence Rate ◽  
Trust Region Method ◽  
Trust Region ◽  
Region Method ◽  
Rate Analysis ◽  
Convergence Rate Analysis
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