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.
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Pré-publication, Document de travail
2018
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  • HAL Id : hal-01708905, version 1

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

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