Volume 53, pp. 459-480, 2020.

The minimal-norm Gauss-Newton method and some of its regularized variants

Federica Pes and Giuseppe Rodriguez


Nonlinear least-squares problems appear in many real-world applications. When a nonlinear model is used to reproduce the behavior of a physical system, the unknown parameters of the model can be estimated by fitting experimental observations by a least-squares approach. It is common to solve such problems by Newton's method or one of its variants such as the Gauss-Newton algorithm. In this paper, we study the computation of the minimal-norm solution to a nonlinear least-squares problem, as well as the case where the solution minimizes a suitable semi-norm. Since many important applications lead to severely ill-conditioned least-squares problems, we also consider some regularization techniques for their solution. Numerical experiments, both artificial and derived from an application in applied geophysics, illustrate the performance of the different approaches.

Full Text (PDF) [516 KB], BibTeX

Key words

nonlinear least-squares, nonlinear inverse problem, regularization, Gauss-Newton method

AMS subject classifications

65F22, 65H10, 65F20

Links to the cited ETNA articles

[8]Vol. 51 (2019), pp. 274-314 Christian Clason and Vu Huu Nhu: Bouligand-Levenberg-Marquardt iteration for a non-smooth ill-posed inverse problem
[10]Vol. 47 (2017), pp. 1-17 Gian Piero Deidda, Patricia Díaz de Alba, and Giuseppe Rodriguez: Identifying the magnetic permeability in multi-frequency EM data inversion

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