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Accelerated derivative-free nonlinear least-squares applied to the estimation of Manning coefficients

Author

Listed:
  • E. G. Birgin

    (University of São Paulo)

  • J. M. Martínez

    (State University of Campinas)

Abstract

A general framework for solving nonlinear least squares problems without the employment of derivatives is proposed in the present paper together with a new general global convergence theory. With the aim to cope with the case in which the number of variables is big (for the standards of derivative-free optimization), two dimension-reduction procedures are introduced. One of them is based on iterative subspace minimization and the other one is based on spline interpolation with variable nodes. Each iteration based on those procedures is followed by an acceleration step inspired in the Sequential Secant Method. The practical motivation for this work is the estimation of parameters in Hydraulic models applied to dam breaking problems. Numerical examples of the application of the new method to those problems are given.

Suggested Citation

  • E. G. Birgin & J. M. Martínez, 2022. "Accelerated derivative-free nonlinear least-squares applied to the estimation of Manning coefficients," Computational Optimization and Applications, Springer, vol. 81(3), pages 689-715, April.
    • Handle: RePEc:spr:coopap:v:81:y:2022:i:3:d:10.1007_s10589-021-00344-w
    DOI: 10.1007/s10589-021-00344-w
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    References listed on IDEAS

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    1. Hongchao Zhang & Andrew Conn, 2012. "On the local convergence of a derivative-free algorithm for least-squares minimization," Computational Optimization and Applications, Springer, vol. 51(2), pages 481-507, March.
    2. Nicolas Boutet & Rob Haelterman & Joris Degroote, 2021. "Secant Update generalized version of PSB: a new approach," Computational Optimization and Applications, Springer, vol. 78(3), pages 953-982, April.
    3. Varadhan, Ravi & Gilbert, Paul, 2009. "BB: An R Package for Solving a Large System of Nonlinear Equations and for Optimizing a High-Dimensional Nonlinear Objective Function," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i04).
    4. Nicolas Boutet & Rob Haelterman & Joris Degroote, 2020. "Secant update version of quasi-Newton PSB with weighted multisecant equations," Computational Optimization and Applications, Springer, vol. 75(2), pages 441-466, March.
    5. Marguerite Frank & Philip Wolfe, 1956. "An algorithm for quadratic programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 95-110, March.
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