On a new updating rule of the Levenberg-Marquardt parameter
type: Item
instance of: scholarly article
title: On a new updating rule of the Levenberg-Marquardt parameter
zbMATH Open document ID: 1404.65046
author: Ruixue Zhao
author: Jinyan Fan
published in: Journal of Scientific Computing
publication date: 2018-04-12T00:00:00Z
review text: The authors are proposing a change in the Levenberg-Marquardt algorithm for solving systems of nonlinear equations. In the traditional algorithm, the iterate and the specific parameter are updated according to the ratio of the actual reduction to the predicted reduction of the merit function. In the proposed version, the iterate is updated as in the traditional algorithm, while the specific parameter is updated based on the value of the gradient norm of the merit function. It is shown that all limit points of the sequence generated by the new algorithm are stationary points of the merit functions. Moreover, the global convergence and the quadratic convergence under the local error condition are proved.
reviewed by: Dana Petcu
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 6858887
zbMATH Keywords: nonlinear equations
zbMATH Keywords: local error bound
zbMATH Keywords: quadratic convergence
describes a project that uses: minpack
MaRDI profile type: Publication
full work available at URL: s10915-017-0488-6
OpenAlex ID: W2660052857
cites work: Q4433566
cites work: The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence
cites work: A Retrospective Trust Region Algorithm with Trust Region Converging to Zero
cites work: On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption
cites work: A method for the solution of certain non-linear problems in least squares
cites work: An Algorithm for Least-Squares Estimation of Nonlinear Parameters
cites work: Q4148902
cites work: Testing Unconstrained Optimization Software
cites work: Nonlinear least squares — the Levenberg algorithm revisited
cites work: Q4083217
cites work: Tensor Methods for Nonlinear Equations
cites work: Q3998482
cites work: An inexact Levenberg-Marquardt method for large sparse nonlinear least squres
cites work: Q2765625
cites work: Q4538036
cites work: Recent advances in numerical methods for nonlinear equations and nonlinear least squares
cites work: Recent advances in trust region algorithms
cites work: Global complexity bound of the Levenberg–Marquardt method
DOI: 10.1007/S10915-017-0488-6
description: scientific article; zbMATH DE number 6858887