Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/21201
Title: The convergence of a Levenberg-Marquardt method for nonlinear inequalities
Authors: Yin, H
Huang, ZH
Qi, L 
Keywords: Global convergence
Inconsistent
Least l2-norm solution
Levenberg-Marquardt method
Local quadratic convergence
Nonlinear inequalities
Issue Date: 2008
Publisher: Taylor & Francis
Source: Numerical functional analysis and optimization, 2008, v. 29, no. 5-6, p. 687-716 How to cite?
Journal: Numerical functional analysis and optimization 
Abstract: In this paper, we consider the least l2-norm solution for a possibly inconsistent system of nonlinear inequalities. The objective function of the problem is only first-order continuously differentiable. By introducing a new smoothing function, the problem is approximated by a family of parameterized optimization problems with twice continuously differentiable objective functions. Then a Levenberg-Marquardt algorithm is proposed to solve the parameterized smooth optimization problems. It is proved that the algorithm either terminates finitely at a solution of the original inequality problem or generates an infinite sequence. In the latter case, the infinite sequence converges to a least l2-norm solution of the inequality problem. The local quadratic convergence of the algorithm was produced under some conditions.
URI: http://hdl.handle.net/10397/21201
ISSN: 0163-0563
DOI: 10.1080/01630560802099936
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