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

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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
Etat de la publication	Publié - 1 sept. 2012

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10.1007/s10589-011-9446-7

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2 Actif

Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Projet: Recherche
ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire
SARTENAER, A. & TOINT, P.
1/01/87 → …
Projet: Axe de recherche

1 Recherche/Enseignement dans une institution externe
1 Visite à une institution académique externe

Polytechnic University of Hong Kong
Philippe Toint (Chercheur visiteur)
31 janv. 2016 → 14 févr. 2016
Activité: Types de Visite d'une organisation externe › Recherche/Enseignement dans une institution externe
Oxford University
Philippe Toint (Chercheur visiteur)
sept. 2015 → déc. 2015
Activité: Types de Visite d'une organisation externe › Visite à une institution académique externe

Contient cette citation

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title = "Updating the regularization parameter in the adaptive cubic regularization algorithm",

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. {\textcopyright} 2011 Springer Science+Business Media, LLC.",

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Updating the regularization parameter in the adaptive cubic regularization algorithm

Résumé

Accès au document

Complexity in nonlinear optimization

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

Polytechnic University of Hong Kong

Oxford University

Contient cette citation