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On an Elliptical Trust-Region Procedure for Ill-Posed Nonlinear Least-Squares Problems

Stefania Bellavia (stefania.bellavia***at***unifi.it)
Elisa Riccietti (elisa.riccietti***at***enseeiht.fr)

Abstract: In this paper we address the stable numerical solution of ill-posed nonlinear least-squares problems with small residual. We propose an elliptical trust-region reformulation of a Levenberg-Marquardt procedure. Thanks to an appropriate choice of the trust-region radius, the proposed procedure guarantees an automatic choice of the free regularization parameters that, together with a suitable stopping criterion, ensures regularizing properties to the method. Specifically, the proposed procedure generates a sequence that even in case of noisy data has the potential to approach a solution of the unperturbed problem. The case of constrained problems is considered, too. The effectiveness of the procedure is shown on several examples of ill-posed least-squares problems.

Keywords: Ill-posed Nonlinear Least-Squares Problems, Regularization, Nonlinear Stepsize Control, Levenberg-Marquardt Methods, Trust-Region Methods

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

Citation: UniversitÓ di Firenze, Dipartimento di Ingegneria Industriale, Firenze, 50134, Italy, 03/2018

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Entry Submitted: 03/03/2018
Entry Accepted: 03/03/2018
Entry Last Modified: 12/15/2018

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