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FISTA restart using an automatic estimation of the growth parameter

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAUJOL, Jean-François
hal.structure.identifierInstitut National des Sciences Appliquées - Toulouse [INSA Toulouse]
dc.contributor.authorDOSSAL, Charles
hal.structure.identifierInstitut National des Sciences Appliquées - Toulouse [INSA Toulouse]
dc.contributor.authorLABARRIÈRE, Hippolyte
hal.structure.identifierInstitut National des Sciences Appliquées - Toulouse [INSA Toulouse]
dc.contributor.authorRONDEPIERRE, Aude
dc.date.accessioned2024-04-04T02:41:19Z
dc.date.available2024-04-04T02:41:19Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191141
dc.description.abstractEnIn 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.isoen
dc.title.enFISTA restart using an automatic estimation of the growth parameter
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-03153525
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03153525v1
bordeaux.COinSctx_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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