A note on solving nonlinear optimization problems in variable precision

S. Gratton; Ph L. Toint

doi:10.1007/s10589-020-00190-2

A note on solving nonlinear optimization problems in variable precision

S. Gratton, Ph L. Toint

Universite de Namur

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

31 Téléchargements (Pure)

Résumé

This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed by Carter (SIAM J Sci Stat Comput 14(2):368–388, 1993) and by Conn et al. (Trust-region methods. MPS-SIAM series on optimization, SIAM, Philadelphia, 2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control. Numerical experiments are presented indicating that the use of the considered method can bring substantial savings in objective function’s and gradient’s evaluation “energy costs” by efficiently exploiting multi-precision computations.

langue originale	Anglais
Pages (de - à)	917-933
Nombre de pages	17
journal	Computational Optimization and Applications
Volume	76
Numéro de publication	3
Les DOIs	https://doi.org/10.1007/s10589-020-00190-2
Etat de la publication	Publié - 1 juil. 2020

Financement

S. Gratton: Partially supported by 3IA Artificial and Natural Intelligence Toulouse Institute, French “Investing for the Future - PIA3” program under the Grant Agreement ANR-19-PI3A-0004. P. L. Toint: Partially supported by ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02.

Accès au document

10.1007/s10589-020-00190-2

2018_TointP_articleAccepted author manuscript, 184 KBLicense: Non spécifié

Autres fichiers et liens

Link to publication in Scopus

9 Citations
1 Livre
1 Article
1 Papier de travail

Minimizing convex quadratics with variable precision Krylov methods
Gratton, S., Simon, E. & Toint, P., 1 oct. 2020, Dans: Numerical Linear Algebra with Applications. 28, 1, p. e2337 26 p.
Résultats de recherche: Contribution à un journal/une revue › Article › Revue par des pairs

File
Exploiting variable precision in GMRES
Gratton, S., Simon, E., Titley-Peloquin, D. & Toint, P., juil. 2019, 19 p.
Résultats de recherche: Papier de travail

File
Trust-region methods
Conn, A., Gould, N. & Toint, P., 2000, Philadelphia (Pa.): SIAM. 959 p. (MPS/SIAM Series on Optimization)
Résultats de recherche: Livre/Rapport/Revue › Livre

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

2 Discours invité
1 Visite à une institution académique externe

Minimizing convex quadratics with variable precision Krylov methods
Toint, P. (Orateur)
28 nov. 2019
Activité: Discours ou présentation › Discours invité
ENSEEIHT-IRIT
Toint, P. (Chercheur visiteur)
4 nov. 2019 → 8 nov. 2019
Activité: Visite d'une organisation externe › Visite à une institution académique externe
Minimizing convex quadratics with variable precision Krylov methods
Toint, P. (Orateur)
10 oct. 2019
Activité: Discours ou présentation › Discours invité

Contient cette citation

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title = "A note on solving nonlinear optimization problems in variable precision",

abstract = "This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed by Carter (SIAM J Sci Stat Comput 14(2):368–388, 1993) and by Conn et al. (Trust-region methods. MPS-SIAM series on optimization, SIAM, Philadelphia, 2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control. Numerical experiments are presented indicating that the use of the considered method can bring substantial savings in objective function{\textquoteright}s and gradient{\textquoteright}s evaluation “energy costs” by efficiently exploiting multi-precision computations.",

keywords = "High-performance computing, Inexact evaluations, Multi-precision arithmetic, Nonlinear optimization",

author = "S. Gratton and Toint, \{Ph L.\}",

note = "Funding Information: S. Gratton: Partially supported by 3IA Artificial and Natural Intelligence Toulouse Institute, French “Investing for the Future - PIA3” program under the Grant Agreement ANR-19-PI3A-0004. P. L. Toint: Partially supported by ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02. Publisher Copyright: {\textcopyright} 2020, Springer Science+Business Media, LLC, part of Springer Nature.",

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doi = "10.1007/s10589-020-00190-2",

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N2 - This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed by Carter (SIAM J Sci Stat Comput 14(2):368–388, 1993) and by Conn et al. (Trust-region methods. MPS-SIAM series on optimization, SIAM, Philadelphia, 2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control. Numerical experiments are presented indicating that the use of the considered method can bring substantial savings in objective function’s and gradient’s evaluation “energy costs” by efficiently exploiting multi-precision computations.

AB - This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed by Carter (SIAM J Sci Stat Comput 14(2):368–388, 1993) and by Conn et al. (Trust-region methods. MPS-SIAM series on optimization, SIAM, Philadelphia, 2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control. Numerical experiments are presented indicating that the use of the considered method can bring substantial savings in objective function’s and gradient’s evaluation “energy costs” by efficiently exploiting multi-precision computations.

KW - High-performance computing

KW - Inexact evaluations

KW - Multi-precision arithmetic

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ER -

A note on solving nonlinear optimization problems in variable precision

Résumé

Financement

Accès au document

Autres fichiers et liens

Empreinte digitale

Résultat de recherche

Minimizing convex quadratics with variable precision Krylov methods

Exploiting variable precision in GMRES

Trust-region methods

Projets

ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

Activités

Minimizing convex quadratics with variable precision Krylov methods

ENSEEIHT-IRIT

Minimizing convex quadratics with variable precision Krylov methods

Contient cette citation