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A split Levenberg-Marquardt method for large-scale sparse problems

Author

Listed:
  • Nataša Krejić

    (University of Novi Sad)

  • Greta Malaspina

    (University of Novi Sad)

  • Lense Swaenen

    (Mathware department, Sioux Technologies)

Abstract

We consider large-scale nonlinear least squares problems with sparse residuals, each of them depending on a small number of variables. A decoupling procedure which results in a splitting of the original problems into a sequence of independent problems of smaller sizes is proposed and analysed. The smaller size problems are modified in a way that offsets the error made by disregarding dependencies that allow us to split the original problem. The resulting method is a modification of the Levenberg-Marquardt method with smaller computational costs. Global convergence is proved as well as local linear convergence under suitable assumptions on sparsity. The method is tested on the network localization simulated problems with up to one million variables and its efficiency is demonstrated.

Suggested Citation

  • Nataša Krejić & Greta Malaspina & Lense Swaenen, 2023. "A split Levenberg-Marquardt method for large-scale sparse problems," Computational Optimization and Applications, Springer, vol. 85(1), pages 147-179, May.
    • Handle: RePEc:spr:coopap:v:85:y:2023:i:1:d:10.1007_s10589-023-00460-9
    DOI: 10.1007/s10589-023-00460-9
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    References listed on IDEAS

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    1. Roger Behling & Douglas S. Gonçalves & Sandra A. Santos, 2019. "Local Convergence Analysis of the Levenberg–Marquardt Framework for Nonzero-Residue Nonlinear Least-Squares Problems Under an Error Bound Condition," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 1099-1122, December.
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