# Convergence of a relaxed inertial forward-backward algorithm for structured monotone inclusions

Abstract : In a Hilbert space ${\mathcal H}$, we study the convergence properties of a class of relaxed inertial forward-backward algorithms. They aim to solve structured monotone inclusions of the form $Ax + Bx \ni 0$ where $A:{\mathcal H}\to 2^{\mathcal H}$ is a maximally monotone operator and $B:{\mathcal H}\to {\mathcal H}$ is a cocoercive operator. We extend to this class of problems the acceleration techniques initially introduced by Nesterov, then developed by Beck and Teboulle in the case of structured convex minimization (FISTA). As an important element of our approach, we develop an inertial and parametric version of the Krasnoselskii-Mann theorem, where joint adjustment of the inertia and relaxation parameters plays a central role. This study comes as an natural extension of the techniques introduced by the authors for the study of relaxed inertial proximal algorithms. An illustration is given to the inertial Nash equilibration of a game combining non-cooperative and cooperative aspects.
Keywords :
Type de document :
Pré-publication, Document de travail
2018

Littérature citée [46 références]

https://hal.archives-ouvertes.fr/hal-01782016
Contributeur : Alexandre Cabot <>
Soumis le : mardi 1 mai 2018 - 00:50:04
Dernière modification le : lundi 11 juin 2018 - 16:47:25

### Fichier

RIFB, April 30, 2018-FINAL.pdf
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### Identifiants

• HAL Id : hal-01782016, version 1

### Citation

Hedy Attouch, Alexandre Cabot. Convergence of a relaxed inertial forward-backward algorithm for structured monotone inclusions. 2018. 〈hal-01782016〉

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