CONVERGENCE OF DAMPED INERTIAL DYNAMICS GOVERNED BY REGULARIZED MAXIMALLY MONOTONE OPERATORS

Abstract : In a Hilbert space setting, we study the asymptotic behavior, as time $t$ goes to infinity, of the trajectories of a second-order differential equation governed by the Yosida regularization of a maximally monotone operator with time-varying positive index $\lambda(t)$. The dissipative and convergence properties are attached to the presence of a viscous damping term with positive coefficient $\gamma(t)$. A suitable tuning of the parameters $\gamma(t)$ and $\lambda(t)$ makes it possible to prove the weak convergence of the trajectories towards zeros of the operator. When the operator is the subdifferential of a closed convex proper function, we estimate the rate of convergence of the values. These results are in line with the recent articles by Attouch-Cabot, and Attouch-Peypouquet. In this last paper, the authors considered the case $\gamma (t) =\frac{\alpha}{t}$, which is naturally linked to Nesterov's accelerated method. We unify, and often improve the results already present in the literature.
Type de document :
Pré-publication, Document de travail
2017
Liste complète des métadonnées

Littérature citée [30 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01648383
Contributeur : Alexandre Cabot <>
Soumis le : samedi 25 novembre 2017 - 18:24:17
Dernière modification le : jeudi 11 janvier 2018 - 06:27:31

Fichier

AC-Max Mon, Sous-Diff., Nov 20...
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01648383, version 1

Citation

Hedy Attouch, Alexandre Cabot. CONVERGENCE OF DAMPED INERTIAL DYNAMICS GOVERNED BY REGULARIZED MAXIMALLY MONOTONE OPERATORS. 2017. 〈hal-01648383〉

Partager

Métriques

Consultations de la notice

67

Téléchargements de fichiers

19