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Résumé
When solving nonlinear leastsquares problems, it is often useful to regularize the problem using a quadratic term, a practice which is especially common in applications arising in inverse calculations. A solution method derived from a trustregion GaussNewton algorithm is analyzed for such applications, where, contrary to the standard algorithm, the leastsquares subproblem solved at each iteration of the method is rewritten as a quadratic minimization subject to linear equality constraints. This allows the exploitation of duality properties of the associated linearized problems. This paper considers a recent conjugategradientlike method which performs the quadratic minimization in the dual space and produces, in exact arithmetic, the same iterates as those produced by a standard conjugategradients method in the primal space. This dual algorithm is computationally interesting whenever the dimension of the dual space is significantly smaller than that of the primal space, yielding gains in terms of both memory usage and computational cost. The relation between this dual space solver and PSAS (Physicalspace Statistical Analysis System), another wellknown dual space technique used in data assimilation problems, is explained. The use of an effective preconditioning technique is proposed and refined convergence bounds derived, which results in a practical solution method. Finally, stopping rules adequate for a trustregion solver are proposed in the dual space, providing iterates that are equivalent to those obtained with a SteihaugToint truncated conjugategradient method in the primal space. © 2012 Springer Science+Business Media, LLC.
langue originale  Anglais 

Pages (de  à)  125 
Nombre de pages  25 
journal  Computational Optimization and Applications 
Volume  54 
Numéro de publication  1 
Les DOIs  
Etat de la publication  Publié  2013 
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Projets
 2 Actif

Développements de nouvelles méthodes d'optimisation pour l'assimilation de données en océanographie
SARTENAER, A., LALOYAUX, P., TOINT, P., Tshimanga Ilunga, J. & Gürol, S.
1/09/07 → …
Projet: Projet de thèse

ADALGOPT: ADALGOPT  Algorithmes avancés en optimisation nonlinéaire
1/01/87 → …
Projet: Axe de recherche
Activités

Institut National Polytechnique de Toulouse
Philippe Toint (Chercheur visiteur)
2017 → 2019Activité: Types de Visite d'une organisation externe › Recherche/Enseignement dans une institution externe

Parallelizing Weak Constraint 4DVAR?
Philippe Toint (Orateur)
5 oct. 2016Activité: Types de discours ou de présentation › Discours invité

Data Assimilation for Weather Forecasting: Reducing the Curse of Dimensionality
Philippe Toint (Orateur invité)
1 déc. 2015Activité: Types de discours ou de présentation › Présentation orale