Mostrar el registro sencillo del ítem

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAUJOL, Jean-François
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorDOSSAL, Charles
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorRONDEPIERRE, Aude
dc.date.accessioned2024-04-04T02:47:04Z
dc.date.available2024-04-04T02:47:04Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191610
dc.description.abstractEnIn 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.sponsorshipMathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond - ANR-19-CE23-0017
dc.language.isoen
dc.subject.enLyapunov function
dc.subject.enrate of convergence
dc.subject.enODEs
dc.subject.enoptimization
dc.subject.enstrong convexity
dc.subject.enHeavy Ball method
dc.title.enConvergence rates of the Heavy-Ball method for quasi-strongly convex optimization
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Optimisation et contrôle [math.OC]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-02545245
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02545245v1
bordeaux.COinSctx_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


Archivos en el ítem

ArchivosTamañoFormatoVer

No hay archivos asociados a este ítem.

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem