An asymptotically optimal gradient algorithm for quadratic optimization with low computational cost

Anatoly Zhigljavsky 1 Luc Pronzato 2 Elena Bukina 2
1 Cardiff University, School of Mathematics
2 Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe SYSTEMES
SIS - Signal, Images et Systèmes
Abstract : We consider gradient algorithms for minimizing a quadratic function in R^n with large n. We suggest a particular sequence of step-lengthes and demonstrate that the resulting gradient algorithm has a convergence rate comparable with that of Conjugate Gradients and other methods based on the use of Krylov spaces. When the problem is large and sparse, the proposed algorithm can be more efficient than the Conjugate Gradient algorithm in terms of computational cost, as k iterations of the proposed algorithm only require the computation of O(log k) inner products.
Keywords : Quadratic optimization gradient algorithms conjugate gradient arcsine distribution Fibonacci numbers estimation of leading eigenvalues
Type de document :
Article dans une revue
Optimization Letters, Springer Verlag, 2013, 7 (6), pp.1047-1059. 〈10.1007/s11590-012-0491-7〉
Liste complète des métadonnées

Littérature citée [10 références]  Voir  Masquer  Télécharger
https://hal.archives-ouvertes.fr/hal-00630982
Contributeur : Luc Pronzato <>
Soumis le : mardi 11 octobre 2011 - 11:15:43
Dernière modification le : mardi 27 mars 2018 - 17:14:02
Document(s) archivé(s) le : jeudi 12 janvier 2012 - 02:25:50

Fichier

Bukina-P-Z_OPTIMIZATION-HAL.pd...
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

I3S | INSMI | UNICE | TDS-MACS | UNIV-COTEDAZUR

Citation

Anatoly Zhigljavsky, Luc Pronzato, Elena Bukina. An asymptotically optimal gradient algorithm for quadratic optimization with low computational cost. Optimization Letters, Springer Verlag, 2013, 7 (6), pp.1047-1059. 〈10.1007/s11590-012-0491-7〉. 〈hal-00630982〉

Exporter

BibTeX TEI DC DCterms EndNote

Partager

Métriques

Consultations de la notice

248

Téléchargements de fichiers

172

Contact

support.ccsd.cnrs.fr
hal.support@ccsd.cnrs.fr
Logo CCSD