# Convergence of a relaxed inertial proximal algorithm for maximally monotone operators

Abstract : In a Hilbert space ${\mathcal H}$, given $A:{\mathcal H}\to 2^{\mathcal H}$ a maximally monotone operator, we study the convergence properties of a general class of relaxed inertial proximal algorithms. This study aims to extend to the case of the general monotone inclusion $Ax \ni 0$ the acceleration techniques initially introduced by Nesterov in the case of convex minimization. The relaxed form of the proximal algorithms plays a central role. It comes naturally with the regularization of the operator $A$ by its Yosida approximation with a variable parameter, a technique recently introduced by Attouch-Peypouquet for a particular class of inertial proximal algorithms. Our study provides an algorithmic version of the convergence results obtained by Attouch-Cabot in the case of continuous dynamical systems.
Keywords :
Type de document :
Pré-publication, Document de travail
2018

Littérature citée [24 références]

https://hal.archives-ouvertes.fr/hal-01708905
Contributeur : Alexandre Cabot <>
Soumis le : mercredi 14 février 2018 - 11:43:20
Dernière modification le : vendredi 8 juin 2018 - 14:50:07
Document(s) archivé(s) le : mardi 15 mai 2018 - 12:10:51

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RIPA-Feb13_bis, 2018.pdf
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• HAL Id : hal-01708905, version 1

### Citation

Hedy Attouch, Alexandre Cabot. Convergence of a relaxed inertial proximal algorithm for maximally monotone operators . 2018. 〈hal-01708905〉

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