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On Non-stationary Tikhonov procedures for ill-posed nonlinear least squares problems

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

Abstract: In this paper we address the stable numerical solution of ill-posed nonlinear least squares problems with small residual. We propose a non-stationary Tikhonov procedure that produces a sequence that in case of noisy data has the potential to approach a solution of the unperturbed problem. We introduce also a suitable elliptical trust-region reformulation that, thanks to an appropriate choice of the trust-region radius, guarantees an automatic choice of the free regularization parameters. The case of constrained problems is considered, too. Numerical results are provided.

Keywords: Ill-posed nonlinear least squares problems, regularization, nonlinear step- size control, non-stationary iterated Tikhonov method, trust-region methods

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

Citation: Dipartimento di Ingegneria Industriale, UniversitÓ di Firenze, viale G.B. Morgagni 40, 50134 Firenze, 01/2017

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Entry Submitted: 01/04/2017
Entry Accepted: 01/04/2017
Entry Last Modified: 06/28/2017

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