Local convergence analysis of the Levenberg-Marquardt framework for nonzero-residue nonlinear least-squares problems under an error bound condition

Roger Behling (roger.behlingufsc.br)
Douglas S. Gonçalves (douglasmtm.ufsc.br)
Sandra A. Santos (sandraime.unicamp.br)

Abstract: The Levenberg-Marquardt method (LM) is widely used for solving nonlinear systems of equations, as well as nonlinear least-squares prob- lems. In this paper, we consider local convergence issues of the LM 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 LM parameter is shown to be dic- tated 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

Category 1: Nonlinear Optimization (Nonlinear Systems and Least-Squares )

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Entry Submitted: 08/23/2018
Entry Accepted: 08/23/2018
Entry Last Modified: 08/31/2018

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