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 Sept 2012


  • numerical performance
  • unconstrained optimization
  • cubic regularization


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