Approximate invariant subspaces and quasi-Newton optimization methods

Serge Gratton; P.L. Toint

doi:10.1080/10556780902992746

Approximate invariant subspaces and quasi-Newton optimization methods

Serge Gratton, P.L. Toint

Namur Institute for Complex Systems

Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

107 Téléchargements (Pure)

Résumé

New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. A new limited-memory Broyden-Fletcher-Goldfarb-Shanno using approximate secant equations is then derived and its encouraging behaviour illustrated on a small collection of multilevel optimization examples. The smoothing properties of this algorithm are considered next, and automatic generation of approximate eigenvalue information demonstrated. The use of this information for improving algorithmic performance is finally investigated on the same multilevel examples. © 2010 Taylor & Francis.

langue originale	Anglais
Pages (de - à)	507-529
Nombre de pages	23
journal	Optimization Methods and Software
Volume	25
Numéro de publication	4
Les DOIs	https://doi.org/10.1080/10556780902992746
Etat de la publication	Publié - 1 août 2010

Accès au document

10.1080/10556780902992746

gt17_OMSAccepted author manuscript, 537 KB

Autres fichiers et liens

Link to publication in Scopus

3 Citations
2 Article

Observations Thinning In Data Assimilation Computations
Gratton, S., Rincon-Camacho, M., Simon, E. & Toint, P., 2015, Dans: EURO Journal on Computational Optimization. 3, p. 31-51
Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

File
Quasi-Newton updates with weighted secant equations
Gratton, S., Malmedy, V. & Toint, P., 4 juil. 2015, Dans: Optimization Methods and Software. 30, 4, p. 748-755 8 p.
Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

File
143 Téléchargements (Pure)

1 Terminé
1 Actif

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire
Sartenaer, A. (Co-investigateur) & Toint, P. (Co-investigateur)
1/01/87 → …
Projet: Axe de recherche
Optimisation multi-échelle non-linéaire
Sartenaer, A. (Responsable du Projet), Toint, P. (Responsable du Projet), Malmedy, V. (Chercheur), Tomanos, D. (Chercheur) & Weber Mendonca, M. (Chercheur)
1/07/04 → 31/07/11
Projet: Recherche

1 Présentation orale
1 Recherche/Enseignement dans une institution externe

Institut National Polytechnique de Toulouse
Toint, P. (Chercheur visiteur)
2017 → 2019
Activité: Visite d'une organisation externe › Recherche/Enseignement dans une institution externe
Data Assimilation for Weather Forecasting: Reducing the Curse of Dimensionality
Toint, P. (Orateur invité)
1 déc. 2015
Activité: Discours ou présentation › Présentation orale

Contient cette citation

@article{340c413070934797b13f0217dc420791,

title = "Approximate invariant subspaces and quasi-Newton optimization methods",

abstract = "New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. A new limited-memory Broyden-Fletcher-Goldfarb-Shanno using approximate secant equations is then derived and its encouraging behaviour illustrated on a small collection of multilevel optimization examples. The smoothing properties of this algorithm are considered next, and automatic generation of approximate eigenvalue information demonstrated. The use of this information for improving algorithmic performance is finally investigated on the same multilevel examples. {\textcopyright} 2010 Taylor & Francis.",

keywords = " secant equation, multigrid techniques, quasi-Newton methods, Unconstrained optimization",

author = "Serge Gratton and P.L. Toint",

note = "Publication code : FP SB010/2007/11 ; QA 0002.2/001/07/11",

year = "2010",

month = aug,

day = "1",

doi = "10.1080/10556780902992746",

language = "English",

volume = "25",

pages = "507--529",

journal = "Optimization Methods and Software",

publisher = "Taylor & Francis",

number = "4",

}

TY - JOUR

T1 - Approximate invariant subspaces and quasi-Newton optimization methods

AU - Gratton, Serge

AU - Toint, P.L.

N1 - Publication code : FP SB010/2007/11 ; QA 0002.2/001/07/11

PY - 2010/8/1

Y1 - 2010/8/1

N2 - New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. A new limited-memory Broyden-Fletcher-Goldfarb-Shanno using approximate secant equations is then derived and its encouraging behaviour illustrated on a small collection of multilevel optimization examples. The smoothing properties of this algorithm are considered next, and automatic generation of approximate eigenvalue information demonstrated. The use of this information for improving algorithmic performance is finally investigated on the same multilevel examples. © 2010 Taylor & Francis.

AB - New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. A new limited-memory Broyden-Fletcher-Goldfarb-Shanno using approximate secant equations is then derived and its encouraging behaviour illustrated on a small collection of multilevel optimization examples. The smoothing properties of this algorithm are considered next, and automatic generation of approximate eigenvalue information demonstrated. The use of this information for improving algorithmic performance is finally investigated on the same multilevel examples. © 2010 Taylor & Francis.

KW - secant equation

KW - multigrid techniques

KW - quasi-Newton methods

KW - Unconstrained optimization

UR - http://www.scopus.com/inward/record.url?scp=77951197373&partnerID=8YFLogxK

U2 - 10.1080/10556780902992746

DO - 10.1080/10556780902992746

M3 - Article

VL - 25

SP - 507

EP - 529

JO - Optimization Methods and Software

JF - Optimization Methods and Software

IS - 4

ER -

Approximate invariant subspaces and quasi-Newton optimization methods

Résumé

Accès au document

Autres fichiers et liens

Empreinte digitale

Résultat de recherche

Observations Thinning In Data Assimilation Computations

Quasi-Newton updates with weighted secant equations

Projets

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

Optimisation multi-échelle non-linéaire

Activités

Institut National Polytechnique de Toulouse

Data Assimilation for Weather Forecasting: Reducing the Curse of Dimensionality

Contient cette citation