The Differential Inclusion Modeling FISTA Algorithm and Optimality of Convergence Rate in the Case b<3
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | APIDOPOULOS, Vassilis | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AUJOL, Jean-François | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DOSSAL, Charles | |
| dc.date.accessioned | 2024-04-04T03:08:52Z | |
| dc.date.available | 2024-04-04T03:08:52Z | |
| dc.date.created | 2017-05-07 | |
| dc.date.issued | 2018-02-22 | |
| dc.identifier.issn | 1052-6234 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193564 | |
| dc.description.abstractEn | 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 Rd, where F is a proper, convex, lower semi-continuous function. The motivation of this study is that the differential inclusion models the FISTA algorithm as considered in [18]. In particular we investigate the different asymptotic properties of solutions for this inclusion for b > 0. We show that the convergence rate of F (x(t)) towards the minimum of F is of order of O(t− 2b/3) when 0 < b < 3, while for b > 3 this order is of o(t−2) and 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], [7], [11] and [31]. In addition we show that order of the convergence rate O(t− 2b/3) of F(x(t)) towards the minimum is optimal, in the case of low friction b < 3, by making a particular choice of F. | |
| dc.description.sponsorship | Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010 | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.subject.en | asymptotic behavior | |
| dc.subject.en | fast minimization | |
| dc.subject.en | differential inclusion | |
| dc.subject.en | FISTA algorithm | |
| dc.subject.en | Convex optimization | |
| dc.title.en | The Differential Inclusion Modeling FISTA Algorithm and Optimality of Convergence Rate in the Case b<3 | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1137/17M1128642 | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| bordeaux.journal | SIAM Journal on Optimization | |
| bordeaux.page | 551–574 | |
| bordeaux.volume | 28 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01517708 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01517708v1 | |
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