A variant of the Levenberg-Marquardt method with adaptive parameters for systems of nonlinear equations

Lin Zheng; Liang Chen; Yanfang Ma

doi:10.3934/math.2022073

journal article Jan 01, 2021

A variant of the Levenberg-Marquardt method with adaptive parameters for systems of nonlinear equations

Lin Zheng

Liang Chen

Yanfang Ma

AIMS Mathematics Vol. 7 No. 1 pp. 1241-1256 · American Institute of Mathematical Sciences (AIMS)

View at Publisher Save 10.3934/math.2022073

Abstract

<abstract>The Levenberg-Marquardt method is one of the most important methods for solving systems of nonlinear equations and nonlinear least-squares problems. It enjoys a quadratic convergence rate under the local error bound condition. Recently, to solve nonzero-residue nonlinear least-squares problem, Behling et al. propose a modified Levenberg-Marquardt method with at least superlinearly convergence under a new error bound condtion [<xref ref-type="bibr" rid="b3">3</xref>]. To extend their results for systems of nonlinear equations, by choosing the LM parameters adaptively, we propose an efficient variant of the Levenberg-Marquardt method and prove its quadratic convergence under the new error bound condition. We also investigate its global convergence by using the Wolfe line search. The effectiveness of the new method is validated by some numerical experiments.</abstract>

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A modified Levenberg–Marquardt method for solving system of nonlinear equations

Liang Chen, Yanfang Ma · 2022

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Details

Published: Jan 01, 2021
Vol/Issue: 7(1)
Pages: 1241-1256

Authors

Nanjing University

School of Chinese Medicine, Hong Kong Baptist University Hong Kong China

Cite This Article

Lin Zheng, Liang Chen, Yanfang Ma (2021). A variant of the Levenberg-Marquardt method with adaptive parameters for systems of nonlinear equations. AIMS Mathematics, 7(1), 1241-1256. https://doi.org/10.3934/math.2022073

A variant of the Levenberg-Marquardt method with adaptive parameters for systems of nonlinear equations

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