A modified Levenberg-Marquardt method with line search for nonlinear equations
type: Item
instance of: scholarly article
title: A modified Levenberg-Marquardt method with line search for nonlinear equations
zbMATH Open document ID: 1356.65152
author: Liang Chen
published in: Computational Optimization and Applications
publication date: 2016-12-15T00:00:00Z
review text: To save more Jacobian calculations and achieve a faster convergence rate a new modified Levenberg-Marquardt (LM) method for nonlinear equations is presented. At every iteration, not only the accelerating trial step but also an additional LM step which uses the previous available Jacobian instead of the new Jacobian, is computed in this new method. Under the local error bound condition which is weaker than nonsingularity, the new method has fourth convergence rate. Results of numerical tests are given.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 6663701
zbMATH Keywords: unconstrained optimization
zbMATH Keywords: nonlinear equations
zbMATH Keywords: Levenberg-Marquardt method
zbMATH Keywords: local error bound
zbMATH Keywords: line search
zbMATH Keywords: convergence
zbMATH Keywords: numerical test
reviewed by: Anton Iliev
describes a project that uses: minpack
MaRDI profile type: Publication
full work available at URL: s10589-016-9852-y
OpenAlex ID: W2405649773
cites work: The effect of calmness on the solution set of systems of nonlinear equations
cites work: The Convergence of a Levenberg–Marquardt Method for Nonlinear Inequalities
cites work: SOME GLOBAL CONVERGENCE PROPERTIES OF THE LEVENBERG-MARQUARDT METHODS WITH LINE SEARCH
cites work: A modified Levenberg-Marquardt method for nonsmooth equations with finitely many maximum functions
cites work: The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence
cites work: Accelerating the modified Levenberg-Marquardt method for nonlinear equations
cites work: A note on the Levenberg-Marquardt parameter
cites work: On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption
cites work: Levenberg–Marquardt methods for parameter estimation problems in the radiative transfer equation
cites work: Levenberg-Marquardt method for solving systems of absolute value equations
cites work: On a regularized Levenberg-Marquardt method for solving nonlinear inverse problems
cites work: A method for the solution of certain non-linear problems in least squares
cites work: A new filter-Levenberg-Marquardt method with disturbance for solving nonlinear complementarity problems
cites work: Convergence analysis of the Levenberg–Marquardt method
cites work: A globally convergent Levenberg-Marquardt method for the least \(l_2\)-norm solution of nonlinear inequalities
cites work: An Algorithm for Least-Squares Estimation of Nonlinear Parameters
cites work: Testing Unconstrained Optimization Software
cites work: Tensor Methods for Nonlinear Equations
cites work: Q3998482
cites work: On a global complexity bound of the Levenberg-marquardt method
cites work: Q2765625
cites work: Q5319776
cites work: A higher-order Levenberg-Marquardt method for nonlinear equations
cites work: A smoothing Levenberg-Marquardt method for the extended linear complementarity problem
cites work: Recent advances in numerical methods for nonlinear equations and nonlinear least squares
cites work: On the convergence of the modified Levenberg-Marquardt method with a nonmonotone second order Armijo type line search
cites work: Affine scaling interior Levenberg-Marquardt method for bound-constrained semismooth equations under local error bound conditions
DOI: 10.1007/S10589-016-9852-Y
description: scientific article