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Algebraic rules for computing the regularization parameter of the Levenberg–Marquardt method

Author

Listed:
  • Elizabeth W. Karas

    (Federal University of Paraná)

  • Sandra A. Santos

    (University of Campinas)

  • Benar F. Svaiter

    (IMPA)

Abstract

This paper presents a class of Levenberg–Marquardt methods for solving the nonlinear least-squares problem. Explicit algebraic rules for computing the regularization parameter are devised. In addition, convergence properties of this class of methods are analyzed. We prove that all accumulation points of the generated sequence are stationary. Moreover, q-quadratic convergence for the zero-residual problem is obtained under an error bound condition. Illustrative numerical experiments with encouraging results are presented.

Suggested Citation

  • Elizabeth W. Karas & Sandra A. Santos & Benar F. Svaiter, 2016. "Algebraic rules for computing the regularization parameter of the Levenberg–Marquardt method," Computational Optimization and Applications, Springer, vol. 65(3), pages 723-751, December.
    • Handle: RePEc:spr:coopap:v:65:y:2016:i:3:d:10.1007_s10589-016-9845-x
    DOI: 10.1007/s10589-016-9845-x
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    References listed on IDEAS

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    1. Ernesto Birgin & Jan Gentil, 2012. "Evaluating bound-constrained minimization software," Computational Optimization and Applications, Springer, vol. 53(2), pages 347-373, October.
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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.

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