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A robust method based on LOVO functions for solving least squares problems

Author

Listed:
  • E. V. Castelani

    (State University of Maringá)

  • R. Lopes

    (State University of Maringá)

  • W. V. I. Shirabayashi

    (State University of Maringá)

  • F. N. C. Sobral

    (State University of Maringá)

Abstract

The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting models to them. This work presents a low order-value optimization (LOVO) version of the Levenberg–Marquardt algorithm, which is well suited to deal with outliers in fitting problems. A general algorithm is presented and convergence to stationary points is demonstrated. Numerical results show that the algorithm is successfully able to detect and ignore outliers without too many specific parameters. Parallel and distributed executions of the algorithm are also possible, allowing the use of larger datasets. Comparison against publicly available robust algorithms shows that the present approach is able to find better adjustments in well known statistical models.

Suggested Citation

  • E. V. Castelani & R. Lopes & W. V. I. Shirabayashi & F. N. C. Sobral, 2021. "A robust method based on LOVO functions for solving least squares problems," Journal of Global Optimization, Springer, vol. 80(2), pages 387-414, June.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:2:d:10.1007_s10898-020-00970-4
    DOI: 10.1007/s10898-020-00970-4
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    References listed on IDEAS

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    1. El Houcine Bergou & Youssef Diouane & Vyacheslav Kungurtsev, 2020. "Convergence and Complexity Analysis of a Levenberg–Marquardt Algorithm for Inverse Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 927-944, June.
    2. E. Birgin & L. Bueno & N. Krejić & J. Martínez, 2011. "Low order-value approach for solving VaR-constrained optimization problems," Journal of Global Optimization, Springer, vol. 51(4), pages 715-742, December.
    3. Zhongyi Jiang & Qiying Hu & Xiaojin Zheng, 2017. "Optimality condition and complexity of order-value optimization problems and low order-value optimization problems," Journal of Global Optimization, Springer, vol. 69(2), pages 511-523, October.
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