Affine scaling interior Levenberg-Marquardt method for bound-constrained semismooth equations under local error bound conditions
type: Item
instance of: scholarly article
title: Affine scaling interior Levenberg-Marquardt method for bound-constrained semismooth equations under local error bound conditions
zbMATH Open document ID: 1151.65047
published in: Journal of Computational and Applied Mathematics
publication date: 2008-08-08T00:00:00Z
review text: An affine scaling Levenberg-Marquardt method with nonmonotonic interior backtracking line search technique for solving bound-constrained semismooth equations under local error bound conditions is presented. Other possible norms (inner products) which may significantly change the computational behaviour (but usually not the convergence rate), effectively providing a preconditioning, are not mentioned. The global convergence results are developed for a semi\-smooth Levenberg-Marquardt method with a backtracking line search technique projecting trial steps onto the feasible interior set. Close to the solution set the algorithm is shown to converge locally Q-superlinearly under some quite weak conditions: The line search as presented is very simple, and maybe computationally very expensive. Overall this is a super-linearly convergent algorithm for non-smooth systems of equations with constraints.
reviewed by: Hermann G. Matthies
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C33
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 5309289
zbMATH Keywords: semismooth equation
zbMATH Keywords: Levenberg-Marquardt method
zbMATH Keywords: affine scaling
zbMATH Keywords: interior point method
zbMATH Keywords: superlinear convergence
zbMATH Keywords: error bounds
zbMATH Keywords: preconditioning
zbMATH Keywords: global convergence
zbMATH Keywords: algorithm
author: Detong Zhu
describes a project that uses: levmar
describes a project that uses: STRSCNE
MaRDI profile type: Publication
full work available at URL: j.cam.2007.07.039
OpenAlex ID: W2009018340
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DOI: 10.1016/J.CAM.2007.07.039
description: scientific article; zbMATH DE number 5309289