Updating the regularization parameter in the adaptive cubic regularization algorithm

Nick Gould, M. Porcelli, Philippe Toint

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The adaptive cubic regularization method (Cartis et al. in Math. Program. Ser. A 127(2):245-295, 2011; Math. Program. Ser. A. 130(2):295-319, 2011) has been recently proposed for solving unconstrained minimization problems. At each iteration of this method, the objective function is replaced by a cubic approximation which comprises an adaptive regularization parameter whose role is related to the local Lipschitz constant of the objective's Hessian. We present new updating strategies for this parameter based on interpolation techniques, which improve the overall numerical performance of the algorithm. Numerical experiments on large nonlinear least-squares problems are provided. © 2011 Springer Science+Business Media, LLC.
Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalComputational Optimization and Applications
Issue number1
Publication statusPublished - 1 Sep 2012


  • numerical performance
  • unconstrained optimization
  • cubic regularization

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  • Projects

    Complexity in nonlinear optimization

    TOINT, P., Gould, N. I. M. & Cartis, C.

    1/11/08 → …

    Project: Research


    • 1 Research/Teaching in a external institution
    • 1 Visiting an external academic institution

    Polytechnic University of Hong Kong

    Philippe Toint (Visiting researcher)

    31 Jan 201614 Feb 2016

    Activity: Visiting an external institution typesResearch/Teaching in a external institution

    Oxford University

    Philippe Toint (Visiting researcher)

    Sep 2015Dec 2015

    Activity: Visiting an external institution typesVisiting an external academic institution

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