On the global convergence of a Levenberg-Marquardt method for constrained nonlinear equations

2004 ◽  
Vol 16 (1-2) ◽  
pp. 183-194 ◽  
Author(s):  
Zhensheng Yu
Keyword(s):  
Global Convergence ◽  
Nonlinear Equations ◽  
Marquardt Method ◽  
Levenberg Marquardt ◽  
Constrained Nonlinear Equations

scholarly journals An inexact Levenberg-Marquardt method for large sparse nonlinear least squres

1985 ◽  
Vol 26 (4) ◽  
pp. 387-403 ◽  
Author(s):  
S. J. Wright ◽  
J. N. Holt
Keyword(s):  
Global Convergence ◽  
Least Squares ◽  
Jacobian Matrix ◽  
Numerical Test ◽  
Convergence Result ◽  
Test Results ◽  
Linear Least Squares ◽  
Optimal Point ◽  
Marquardt Method ◽  
Levenberg Marquardt

AbstractA method for solving problems of the form is presented. The approach of Levenberg and Marquardt is used, except that the linear least squares subproblem arising at each iteration is not solved exactly, but only to within a certain tolerance. The method is most suited to problems in which the Jacobian matrix is sparse. Use is made of the iterative algorithm LSQR of Paige and Saunders for sparse linear least squares.A global convergence result can be proven, and under certain conditions it can be shown that the method converges quadratically when the sum of squares at the optimal point is zero.Numerical test results for problems of varying residual size are given.

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.

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