Heavy Ball Momentum for Non-Strongly Convex Optimization
DOSSAL, Charles
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
LABARRIÈRE, Hippolyte
Università degli studi di Genova = University of Genoa [UniGe]
Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova] [DIBRIS]
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Università degli studi di Genova = University of Genoa [UniGe]
Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova] [DIBRIS]
DOSSAL, Charles
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
LABARRIÈRE, Hippolyte
Università degli studi di Genova = University of Genoa [UniGe]
Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova] [DIBRIS]
Università degli studi di Genova = University of Genoa [UniGe]
Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova] [DIBRIS]
RONDEPIERRE, Aude
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Laboratoire d'analyse et d'architecture des systèmes [LAAS]
< Leer menos
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Laboratoire d'analyse et d'architecture des systèmes [LAAS]
Idioma
en
Document de travail - Pré-publication
Este ítem está publicado en
2024-03-11
Resumen en inglés
When 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 ...Leer más >
When 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.< Leer menos
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