Stability of over-relaxations for the Forward-Backward algorithm, application to FISTA
| 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 | 2024-04-04T03:18:13Z | |
| dc.date.available | 2024-04-04T03:18:13Z | |
| dc.date.created | 2014-10-30 | |
| dc.date.issued | 2015-06-12 | |
| dc.identifier.issn | 1052-6234 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194381 | |
| dc.description.abstractEn | This paper is concerned with the convergence of over-relaxations of FB algorithm (in particular FISTA), in the case when proximal maps and/or gradients are computed with a possible error. We show that provided these errors are small enough, then the algorithm still converges to a minimizer of the functional, and with a speed of convergence (in terms of values of the functional) that remains the same as in the noise free case. We also show that larger errors can be allowed, using a lower over-relaxation than FISTA. This still leads to the convergence of iterates, and with ergodic convergence speed faster than the classical FB algorithm and FISTA. | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.subject.en | Convex analysis | |
| dc.subject.en | proximal operator | |
| dc.subject.en | FISTA | |
| dc.subject.en | FB | |
| dc.subject.en | over-relaxation. | |
| dc.title.en | Stability of over-relaxations for the Forward-Backward algorithm, application to FISTA | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math] | |
| bordeaux.journal | SIAM Journal on Optimization | |
| bordeaux.page | www | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01163432 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01163432v1 | |
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