Trust-region and other regularisations of linear least-squares problems

Coralia Cartis; Nick Gould; Philippe Toint

doi:10.1007/s10543-008-0206-8

Trust-region and other regularisations of linear least-squares problems

Coralia Cartis, Nick Gould, Philippe Toint

Namur Institute for Complex Systems

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Résumé

We consider methods for regularising the least-squares solution of the linear system Ax=b. In particular, we propose iterative methods for solving large problems in which a trust-region bound ||x||Δ is imposed on the size of the solution, and in which the least value of linear combinations of ||Ax-b || and a regularisation term ||x|| for various p and q=1,2 is sought. In each case, one or more "secular" equations are derived, and fast Newton-like solution procedures are suggested. The resulting algorithms are available as part of the G ALAHAD optimization library. © 2009 Springer Science + Business Media B.V.

langue originale	Anglais
Pages (de - à)	21-53
Nombre de pages	33
journal	BIT Numerical Mathematics
Volume	49
Numéro de publication	1
Les DOIs	https://doi.org/10.1007/s10543-008-0206-8
Etat de la publication	Publié - 1 mars 2009

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10.1007/s10543-008-0206-8

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

Contient cette citation

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Trust-region and other regularisations of linear least-squares problems

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Projets

Complexity in nonlinear optimization

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

Contient cette citation