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Heavy Ball Momentum for Non-Strongly Convex Optimization

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAUJOL, Jean-François
hal.structure.identifierInstitut National des Sciences Appliquées - Toulouse [INSA Toulouse]
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorDOSSAL, Charles
hal.structure.identifierUniversità degli studi di Genova = University of Genoa [UniGe]
hal.structure.identifierDipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova] [DIBRIS]
dc.contributor.authorLABARRIÈRE, Hippolyte
hal.structure.identifierInstitut National des Sciences Appliquées - Toulouse [INSA Toulouse]
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
hal.structure.identifierLaboratoire d'analyse et d'architecture des systèmes [LAAS]
dc.contributor.authorRONDEPIERRE, Aude
dc.date.accessioned2024-04-04T02:29:47Z
dc.date.available2024-04-04T02:29:47Z
dc.date.issued2024-03-11
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/190207
dc.description.abstractEnWhen considering the minimization of a quadratic or strongly convex function, it is well known that first-order methods involving an inertial term weighted by a constant-in-time parameter are particularly efficient (see Polyak [32], Nesterov [28], and references therein). By setting the inertial parameter according to the condition number of the objective function, these methods guarantee a fast exponential decay of the error. We prove that this type of schemes (which are later called Heavy Ball schemes) is relevant in a relaxed setting, i.e. for composite functions satisfying a quadratic growth condition. In particular, we adapt V-FISTA, introduced by Beck in [10] for strongly convex functions, to this broader class of functions. To the authors' knowledge, the resulting worst-case convergence rates are faster than any other in the literature, including those of FISTA restart schemes. No assumption on the set of minimizers is required and guarantees are also given in the non-optimal case, i.e. when the condition number is not exactly known. This analysis follows the study of the corresponding continuous-time dynamical system (Heavy Ball with friction system), for which new convergence results of the trajectory are shown.
dc.description.sponsorshipProblèmes inverses aveugles et microscopie optique - ANR-21-CE48-0008
dc.description.sponsorshipMathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond - ANR-19-CE23-0017
dc.description.sponsorshipNumerical analysis, optimal control and optimal transport for AI - ANR-23-PEIA-0004
dc.language.isoen
dc.title.enHeavy Ball Momentum for Non-Strongly Convex Optimization
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]
dc.identifier.arxiv2403.06930
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-04500652
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-04500652v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2024-03-11&rft.au=AUJOL,%20Jean-Fran%C3%A7ois&DOSSAL,%20Charles&LABARRI%C3%88RE,%20Hippolyte&RONDEPIERRE,%20Aude&rft.genre=preprint


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