On a second order differential inclusion modeling the FISTA algorithm

Abstract : In this paper we are interested in the differential inclusion 0 ∈ ¨ x(t) + b t ˙ x(t) + ∂F (x(t)) in a finite-dimensional Hilbert space H, where F is a sum of two convex, lower semi-continuous functions with one being differentiable with Lipschitz gradient. The motivation of this study is that the differential inclusion models an accelerated version of proximal gradient algorithm called FISTA. In particular we prove existence of a global solution for this inclusion. Furthermore we show that under the condition b > 3, the convergence rate of F (x(t)) towards the minimimum of F is of order of o t −2 and that the solution-trajectory converges to a minimizer of F. These results generalize the ones obtained in the differential setting (where F is differentiable) in [6].
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01517708
Contributeur : Vasileios Apidopoulos <>
Soumis le : mercredi 3 mai 2017 - 17:33:53
Dernière modification le : mercredi 10 mai 2017 - 01:05:49

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  • HAL Id : hal-01517708, version 1

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Vassilis Apidopoulos, Jean-François Aujol, Charles Dossal. On a second order differential inclusion modeling the FISTA algorithm. 2017. <hal-01517708>

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