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On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation

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Abstract

In this paper we address the stable numerical solution of nonlinear ill-posed systems by a trust-region method. We show that an appropriate choice of the trust-region radius gives rise to a procedure that has the potential to approach a solution of the unperturbed system. This regularizing property is shown theoretically and validated numerically.

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Acknowledgments

Work partially supported by INdAM-GNCS, under the 2015 Project “Metodi di regolarizzazione per problemi di ottimizzazione e applicazioni”.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Industriale, Università di Firenze, viale G.B. Morgagni 40, 50134, Firenze, Italy

    S. Bellavia & B. Morini

  2. Dipartimento di Matematica e Informatica “Ulisse Dini”, Università di Firenze, viale G.B. Morgagni 67a, 50134, Firenze, Italy

    E. Riccietti

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  1. S. Bellavia
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  2. B. Morini
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  3. E. Riccietti
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Correspondence to S. Bellavia.

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Bellavia, S., Morini, B. & Riccietti, E. On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation. Comput Optim Appl 64, 1–30 (2016). https://doi.org/10.1007/s10589-015-9806-9

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