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 › Revue par des pairs

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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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31 Citations
3 Article
1 Livre
1 Article de travail

Evaluation complexity of algorithms for nonconvex optimization
Cartis, C., Gould, N. I. M. & TOINT, P., juil. 2022, SIAM. 600 p. (SIAM-MOS Series on Optimization)
Résultats de recherche: Livre/Rapport/Revue › Livre
Adaptive regularization algorithms with inexact evaluations for nonconvex optimization
Bellavia, S., Gurioli, G., Morini, B. & Toint, P., 2 janv. 2020, Dans: SIAM Journal on Optimization. 29, 4, p. 2881-2915 35 p.
Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

Accès ouvert
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Second-order optimality and beyond: Characterization and Evaluation Complexity in Convexly Constrained Nonlinear Optimization
Cartis, C., Gould, N. I. M. & Toint, P., 1 oct. 2018, Dans: Foundations of Computational Mathematics. 18, 5, p. 1073-1107 35 p.
Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

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

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

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Updating the regularization parameter in the adaptive cubic regularization algorithm

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Résultat de recherche

Evaluation complexity of algorithms for nonconvex optimization

Adaptive regularization algorithms with inexact evaluations for nonconvex optimization

Second-order optimality and beyond: Characterization and Evaluation Complexity in Convexly Constrained Nonlinear Optimization

Projets

Complexity in nonlinear optimization

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

Activités

Hong Kong Polytechnic University

University of Oxford

Contient cette citation