On the convergence of a trust-region method for solving constrained nonlinear equations with degenerate solutions
type: Item
instance of: scholarly article
title: On the convergence of a trust-region method for solving constrained nonlinear equations with degenerate solutions
zbMATH Open document ID: 1069.65055
author: Liqun Qi
author: Xiaojiao Tong
published in: Journal of Optimization Theory and Applications
publication date: 2005-04-07T00:00:00Z
review text: The authors discuss a so called trust-region method for the numerical solving of a system of constrained nonlinear equations. The new method can be regarded as an extension of the work of the authors [ibid. 120, No. 3, 601--625 (2004; Zbl 1140.65331)] and of the method of \textit{C. Kanzow} [Complementarity: Applications, Algorithms and Extensions (Kluwer Academic Publishers, Dordrecht), 179--200 (2001; Zbl 0983.90060)]. The proposed method is globally convergent. Local superlinear and quadratic convergence of the algorithm under the condition of a local error bound, are proved. Eight numerical examples taken from the literature are performed by the proposed method, and the results are promising. In most of the examples, the iterative sequence converges to the solution quickly.
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 2153863
zbMATH Keywords: constrained nonlinear equations
zbMATH Keywords: trust-region methods
zbMATH Keywords: global convergence
zbMATH Keywords: superlinear/quadratic convergence
zbMATH Keywords: error bounds
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
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full work available at URL: b:jota.0000043997.42194.dc
OpenAlex ID: W2088806118
DOI: 10.1023/B:JOTA.0000043997.42194.DC
description: scientific article; zbMATH DE number 2153863