Updating the regularization parameter in the adaptive cubic regularization algorithm

Nick Gould; M. Porcelli; Philippe Toint

doi:10.1007/s10589-011-9446-7

Updating the regularization parameter in the adaptive cubic regularization algorithm

Nick Gould, M. Porcelli, Philippe Toint

Résultats de recherche: Contribution à un journal/une revue › Article

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Résumé

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.

langue originale	Anglais
Pages (de - à)	1-22
Nombre de pages	22
journal	Computational Optimization and Applications
Volume	53
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s10589-011-9446-7
état	Publié - 1 sept. 2012

Empreinte digitale

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

Citer ceci

Gould, N., Porcelli, M., & Toint, P. (2012). Updating the regularization parameter in the adaptive cubic regularization algorithm. Computational Optimization and Applications, 53(1), 1-22. https://doi.org/10.1007/s10589-011-9446-7

Gould, Nick ; Porcelli, M. ; Toint, Philippe. / Updating the regularization parameter in the adaptive cubic regularization algorithm. Dans: Computational Optimization and Applications. 2012 ; Vol 53, Numéro 1. p. 1-22.

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Gould, N, Porcelli, M & Toint, P 2012, 'Updating the regularization parameter in the adaptive cubic regularization algorithm', Computational Optimization and Applications, VOL. 53, Numéro 1, p. 1-22. https://doi.org/10.1007/s10589-011-9446-7

Updating the regularization parameter in the adaptive cubic regularization algorithm. / Gould, Nick; Porcelli, M.; Toint, Philippe.

Dans: Computational Optimization and Applications, Vol 53, Numéro 1, 01.09.2012, p. 1-22.

Résultats de recherche: Contribution à un journal/une revue › Article

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AB - 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.

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