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

Author

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  • S. Bellavia

    (Università di Firenze)

  • B. Morini

    (Università di Firenze)

  • E. Riccietti

    (Università di Firenze)

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.

Suggested Citation

  • S. Bellavia & B. Morini & E. Riccietti, 2016. "On an adaptive regularization for ill-posed nonlinear systems and its trust-region implementation," Computational Optimization and Applications, Springer, vol. 64(1), pages 1-30, May.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:1:d:10.1007_s10589-015-9806-9
    DOI: 10.1007/s10589-015-9806-9
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    References listed on IDEAS

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    1. Ju-liang Zhang & Yong Wang, 2003. "A new trust region method for nonlinear equations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 283-298, November.
    2. Jinyan Fan & Jianyu Pan, 2011. "An improved trust region algorithm for nonlinear equations," Computational Optimization and Applications, Springer, vol. 48(1), pages 59-70, January.
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    Cited by:

    1. Stefania Bellavia & Elisa Riccietti, 2018. "On an Elliptical Trust-Region Procedure for Ill-Posed Nonlinear Least-Squares Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 824-859, September.
    2. Boos, Everton & Gonçalves, Douglas S. & Bazán, Fermín S.V., 2024. "Levenberg-Marquardt method with singular scaling and applications," Applied Mathematics and Computation, Elsevier, vol. 474(C).

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