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Levenberg–Marquardt method based on probabilistic Jacobian models for nonlinear equations

Author

Listed:
  • Ruixue Zhao

    (Shanghai University of Finance and Economics)

  • Jinyan Fan

    (Shanghai Jiao Tong University)

Abstract

In this paper, we propose a Levenberg–Marquardt method based on probabilistic models for nonlinear equations for which the Jacobian cannot be computed accurately or the computation is very expensive. We introduce the definition of the first-order accurate probabilistic Jacobian model, and show how to construct such a model with sample points generated by standard Gaussian distribution. Under certain conditions, we prove that the proposed method converges to a first order stationary point with probability one. Numerical results show the efficiency of the method.

Suggested Citation

  • Ruixue Zhao & Jinyan Fan, 2022. "Levenberg–Marquardt method based on probabilistic Jacobian models for nonlinear equations," Computational Optimization and Applications, Springer, vol. 83(2), pages 381-401, November.
    • Handle: RePEc:spr:coopap:v:83:y:2022:i:2:d:10.1007_s10589-022-00393-9
    DOI: 10.1007/s10589-022-00393-9
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    References listed on IDEAS

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    1. NESTEROV, Yurii, 2011. "Random gradient-free minimization of convex functions," LIDAM Discussion Papers CORE 2011001, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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