On an Elliptical Trust-Region Procedure for Ill-Posed Nonlinear Least-Squares Problems |
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Authors: | Stefania Bellavia Elisa Riccietti |
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Institution: | 1.Dipartimento di Ingegneria Industriale,Università di Firenze,Florence,Italy;2.Institut de Recherche en Informatique de Toulouse (IRIT),Toulouse,France |
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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. |
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