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.
On an Elliptical Trust-Region Procedure for Ill-Posed Nonlinear Least-Squares Problems / Stefania Bellavia, Elisa Riccietti. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - STAMPA. - 178:(2018), pp. 824-859. [10.1007/s10957-018-1318-1]
On an Elliptical Trust-Region Procedure for Ill-Posed Nonlinear Least-Squares Problems
Stefania Bellavia
;
2018
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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.