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Convergence properties of Levenberg–Marquardt methods with generalized regularization terms

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  • Ariizumi, Shumpei
  • Yamakawa, Yuya
  • Yamashita, Nobuo

Abstract

Levenberg–Marquardt methods (LMMs) are the most typical algorithms for solving nonlinear equations F(x)=0, where F:Rn→Rm is a continuously differentiable function. They sequentially solve subproblems represented as squared residual of the Newton equations with the L2 regularization to determine the search direction. However, since the subproblems of the LMMs are usually reduced to linear equations with n variables, it takes much time to solve them when m≪n.

Suggested Citation

  • Ariizumi, Shumpei & Yamakawa, Yuya & Yamashita, Nobuo, 2024. "Convergence properties of Levenberg–Marquardt methods with generalized regularization terms," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    • Handle: RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005349
    DOI: 10.1016/j.amc.2023.128365
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    References listed on IDEAS

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    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    2. NESTEROV, Yurii & POLYAK, B.T., 2006. "Cubic regularization of Newton method and its global performance," LIDAM Reprints CORE 1927, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Andreas Fischer & Alexey F. Izmailov & Mikhail V. Solodov, 2024. "The Levenberg–Marquardt method: an overview of modern convergence theories and more," Computational Optimization and Applications, Springer, vol. 89(1), pages 33-67, September.

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