Algebraic rules for computing the regularization parameter of the Levenberg–Marquardt method

Elizabeth W. Karas (), Sandra A. Santos and Benar F. Svaiter
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Elizabeth W. Karas: Federal University of Paraná
Sandra A. Santos: University of Campinas
Benar F. Svaiter: IMPA

Computational Optimization and Applications, 2016, vol. 65, issue 3, No 8, 723-751

Abstract: Abstract This paper presents a class of Levenberg–Marquardt methods for solving the nonlinear least-squares problem. Explicit algebraic rules for computing the regularization parameter are devised. In addition, convergence properties of this class of methods are analyzed. We prove that all accumulation points of the generated sequence are stationary. Moreover, q-quadratic convergence for the zero-residual problem is obtained under an error bound condition. Illustrative numerical experiments with encouraging results are presented.

Keywords: Nonlinear least-squares problems; Levenberg–Marquardt method; Regularization; Global convergence; Local convergence; Computational results; 90C30; 65K05; 49M37 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-016-9845-x

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