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On an Elliptical Trust-Region Procedure for Ill-Posed Nonlinear Least-Squares Problems

Author

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  • Stefania Bellavia

    (Università di Firenze)

  • Elisa Riccietti

    (Institut de Recherche en Informatique de Toulouse (IRIT))

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:3:d:10.1007_s10957-018-1318-1
    DOI: 10.1007/s10957-018-1318-1
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Roger Behling & Douglas S. Gonçalves & Sandra A. Santos, 2019. "Local Convergence Analysis of the Levenberg–Marquardt Framework for Nonzero-Residue Nonlinear Least-Squares Problems Under an Error Bound Condition," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1099-1122, December.
    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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    1. 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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