Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/5882
Title: Global convergence of a new hybrid Gauss-Newton structured BFGS method for nonlinear least squares problems
Authors: Zhou, W
Chen, X 
Keywords: Nonlinear least squares
Gauss–Newton method
BFGS method
Structured quasi-Newton method
Global convergence
Quadratic convergence
Issue Date: 2010
Publisher: Society for Industrial and Applied Mathematics
Source: SIAM journal on optimization, 2010, v. 20, no. 5, p. 2422–2441 How to cite?
Journal: SIAM Journal on optimization 
Abstract: In this paper, we propose a hybrid Gauss–Newton structured BFGS method with a new update formula and a new switch criterion for the iterative matrix to solve nonlinear least squares problems. We approximate the second term in the Hessian by a positive definite BFGS matrix. Under suitable conditions, global convergence of the proposed method with a backtracking line search is established. Moreover, the proposed method automatically reduces to the Gauss–Newton method for zero residual problems and the structured BFGS method for nonzero residual problems in a neighborhood of an accumulation point. A locally quadratic convergence rate for zero residual problems and a locally superlinear convergence rate for nonzero residual problems are obtained for the proposed method. Some numerical results are given to compare the proposed method with some existing methods.
URI: http://hdl.handle.net/10397/5882
ISSN: 1052-6234
EISSN: 1095-7189
DOI: 10.1137/090748470
Rights: © 2010 Society for Industrial and Applied Mathematics
Appears in Collections:Journal/Magazine Article

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