Levenberg--Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints
type: Item
instance of: scholarly article
title: Levenberg--Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints
zbMATH Open document ID: 1064.65037
author: Christian Kanzow
author: Nobuo Yamashita
author: Masao Fukushima
published in: Journal of Computational and Applied Mathematics
publication date: 2005-01-13T00:00:00Z
review text: Two Levenberg-Marquardt algorithms are considered for the solution of a, not necessarily square, system of nonlinear equations with convex constraints. Motivated by an earlier paper of \textit{N. Yamashita} and \textit{M. Fukushima} [Comput. Suppl. 15, 239--249 (2001; Zbl 1001.65047)] the usual nonsingularity assumption is replaced by an error bound condition that allows the solution set to be (locally) nonunique. At each step, one of the algorithms solves a strictly convex minimization problem, while the other requires only the solution of one system of linear equations. Both methods are shown to converge locally quadratically. Some numerical examples for the second method are given.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 2127102
zbMATH Keywords: constraint equation
zbMATH Keywords: Levenberg-Marquardt method
zbMATH Keywords: projected gradient
zbMATH Keywords: quadratic convergence
zbMATH Keywords: error bounds
zbMATH Keywords: algorithm
zbMATH Keywords: convex minimization
zbMATH Keywords: numerical examples
Wikidata QID: Q56443832
reviewed by: Werner C. Rheinboldt
describes a project that uses: STRSCNE
describes a project that uses: levmar
MaRDI profile type: Publication
full work available at URL: j.cam.2004.02.013
OpenAlex ID: W4205236922
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DOI: 10.1016/J.CAM.2004.02.013
description: scientific article; zbMATH DE number 2127102