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Convergence rates of the Heavy-Ball method for quasi-strongly convex optimization
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | AUJOL, Jean-François | |
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| dc.contributor.author | DOSSAL, Charles | |
| hal.structure.identifier | Institut de Mathématiques de Toulouse UMR5219 [IMT] | |
| dc.contributor.author | RONDEPIERRE, Aude | |
| dc.date.accessioned | 2024-04-04T02:47:04Z | |
| dc.date.available | 2024-04-04T02:47:04Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191610 | |
| dc.description.abstractEn | In this paper, we study the behavior of solutions of the ODE associated to the Heavy Ball method. Since the pioneering work of B.T. Polyak [25], it is well known that such a scheme is very efficient for C2 strongly convex functions with Lipschitz gradient. But much less is known when the C2 assumption is dropped. Depending on the geometry of the function to minimize, we obtain optimal convergence rates for the class of convex functions with some additional regularity such as quasi-strong convexity or strong convexity. We perform this analysis in continuous time for the ODE, and then we transpose these results for discrete optimization schemes. In particular, we propose a variant of the Heavy Ball algorithm which has the best state of the art convergence rate for first order methods to minimize strongly, composite non smooth convex functions. | |
| dc.description.sponsorship | Mathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond - ANR-19-CE23-0017 | |
| dc.language.iso | en | |
| dc.subject.en | Lyapunov function | |
| dc.subject.en | rate of convergence | |
| dc.subject.en | ODEs | |
| dc.subject.en | optimization | |
| dc.subject.en | strong convexity | |
| dc.subject.en | Heavy Ball method | |
| dc.title.en | Convergence rates of the Heavy-Ball method for quasi-strongly convex optimization | |
| 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-02545245 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02545245v1 | |
| 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&RONDEPIERRE,%20Aude&rft.genre=preprint |
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