Local Convergence Analysis of the Levenberg–Marquardt Framework for Nonzero-Residue Nonlinear Least-Squares Problems Under an Error Bound Condition

Roger Behling (), Douglas S. Gonçalves () and Sandra A. Santos ()
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Roger Behling: Fundação Getúlio Vargas
Douglas S. Gonçalves: Federal University of Santa Catarina
Sandra A. Santos: University of Campinas

Journal of Optimization Theory and Applications, 2019, vol. 183, issue 3, No 15, 1099-1122

Abstract: Abstract The Levenberg–Marquardt method is widely used for solving nonlinear systems of equations, as well as nonlinear least-squares problems. In this paper, we consider local convergence properties of the method, when applied to nonzero-residue nonlinear least-squares problems under an error bound condition, which is weaker than requiring full rank of the Jacobian in a neighborhood of a stationary point. Differently from the zero-residue case, the choice of the Levenberg–Marquardt parameter is shown to be dictated by (i) the behavior of the rank of the Jacobian and (ii) a combined measure of nonlinearity and residue size in a neighborhood of the set of (possibly non-isolated) stationary points of the sum of squares function.

Keywords: Local convergence; Levenberg–Marquardt method; Nonlinear least-squares; Nonzero residue; Error bound; 49M37; 65K05; 90C30 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-019-01586-9

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