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Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations

Author

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  • A. Fischer

    (Technische Universität Dresden)

  • A. F. Izmailov

    (Lomonosov Moscow State University, MSU)

  • M. V. Solodov

    (IMPA – Instituto de Matemática Pura e Aplicada)

Abstract

In the case of singular (and possibly even nonisolated) solutions of nonlinear equations, while superlinear convergence of the Newton method cannot be guaranteed, local linear convergence from large domains of starting points still holds under certain reasonable assumptions. We consider a linesearch globalization of the Newton method, combined with extrapolation and over-relaxation accelerating techniques, aiming at a speed up of convergence to critical solutions (a certain class of singular solutions). Numerical results indicate that an acceleration is observed indeed.

Suggested Citation

  • A. Fischer & A. F. Izmailov & M. V. Solodov, 2021. "Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations," Computational Optimization and Applications, Springer, vol. 78(1), pages 273-286, January.
    • Handle: RePEc:spr:coopap:v:78:y:2021:i:1:d:10.1007_s10589-020-00230-x
    DOI: 10.1007/s10589-020-00230-x
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    References listed on IDEAS

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    1. Francisco Facchinei & Andreas Fischer & Markus Herrich, 2013. "A family of Newton methods for nonsmooth constrained systems with nonisolated solutions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 433-443, June.
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    Cited by:

    1. A. Fischer & A. F. Izmailov & M. Jelitte, 2021. "Newton-type methods near critical solutions of piecewise smooth nonlinear equations," Computational Optimization and Applications, Springer, vol. 80(2), pages 587-615, November.

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