FISTA restart using an automatic estimation of the growth parameter
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AUJOL, Jean-François | |
| hal.structure.identifier | Institut National des Sciences Appliquées - Toulouse [INSA Toulouse] | |
| dc.contributor.author | DOSSAL, Charles | |
| hal.structure.identifier | Institut National des Sciences Appliquées - Toulouse [INSA Toulouse] | |
| dc.contributor.author | LABARRIÈRE, Hippolyte | |
| hal.structure.identifier | Institut National des Sciences Appliquées - Toulouse [INSA Toulouse] | |
| dc.contributor.author | RONDEPIERRE, Aude | |
| dc.date.accessioned | 2024-04-04T02:41:19Z | |
| dc.date.available | 2024-04-04T02:41:19Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191141 | |
| dc.description.abstractEn | In this paper, we propose a restart scheme for FISTA (Fast Iterative Shrinking-Threshold Algorithm). This method which is a generalization of Nesterov's accelerated gradient algorithm is widely used in the field of large convex optimization problems and it provides fast convergence results under a strong convexity assumption. These convergence rates can be extended for weaker hypotheses such as the \L{}ojasiewicz property but it requires prior knowledge on the function of interest. In particular, most of the schemes providing a fast convergence for non-strongly convex functions satisfying a quadratic growth condition involve the growth parameter which is generally not known. Recent works show that restarting FISTA could ensure a fast convergence for this class of functions without requiring any knowledge on the growth parameter. We improve these restart schemes by providing a better asymptotical convergence rate and by requiring a lower computation cost. We present numerical results emphasizing the efficiency of this method. | |
| dc.language.iso | en | |
| dc.title.en | FISTA restart using an automatic estimation of the growth parameter | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Optimisation et contrôle [math.OC] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03153525 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03153525v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=AUJOL,%20Jean-Fran%C3%A7ois&DOSSAL,%20Charles&LABARRI%C3%88RE,%20Hippolyte&RONDEPIERRE,%20Aude&rft.genre=preprint |
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