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On a Global Complexity Bound of the Levenberg-Marquardt Method

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Abstract

In this paper, we investigate a global complexity bound of the Levenberg-Marquardt method (LMM) for the nonlinear least squares problem. The global complexity bound for an iterative method solving unconstrained minimization of φ is an upper bound to the number of iterations required to get an approximate solution, such that ‖∇φ(x)‖≤ε. We show that the global complexity bound of the LMM is O(ε −2).

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Authors and Affiliations

  1. Advanced Technology R&D Center, Mitsubishi Electric Corporation, Hyogo, 661-8661, Japan

    Kenji Ueda

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Nobuo Yamashita

Authors
  1. Kenji Ueda
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  2. Nobuo Yamashita
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Correspondence to Nobuo Yamashita.

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Communicated by B. Polyak.

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Ueda, K., Yamashita, N. On a Global Complexity Bound of the Levenberg-Marquardt Method. J Optim Theory Appl 147, 443–453 (2010). https://doi.org/10.1007/s10957-010-9731-0

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  • DOI: https://doi.org/10.1007/s10957-010-9731-0

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