Updating the regularization parameter in the adaptive cubic regularization algorithm

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Abstract

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
Volume53
Issue number1
DOIs
Publication statusPublished - 1 Sep 2012

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Regularization Parameter
Updating
Regularization
Interpolation
Nonlinear Least Squares Problem
Unconstrained Minimization
Regularization Method
Minimization Problem
Lipschitz
Industry
Objective function
Experiments
Interpolate
Numerical Experiment
Iteration
Approximation
Strategy
Business

Keywords

  • numerical performance
  • unconstrained optimization
  • cubic regularization

Cite this

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abstract = "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. {\circledC} 2011 Springer Science+Business Media, LLC.",
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Updating the regularization parameter in the adaptive cubic regularization algorithm. / Gould, Nick; Porcelli, M.; Toint, Philippe.

In: Computational Optimization and Applications, Vol. 53, No. 1, 01.09.2012, p. 1-22.

Research output: Contribution to journalArticle

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