Convergence rates of an inertial gradient descent algorithm under growth and flatness conditions
DOSSAL, Charles
Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
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Institut National des Sciences Appliquées - Toulouse [INSA Toulouse]
Institut de Mathématiques de Toulouse UMR5219 [IMT]
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]
RONDEPIERRE, Aude
Institut de Mathématiques de Toulouse UMR5219 [IMT]
Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes [LAAS-ROC]
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Institut de Mathématiques de Toulouse UMR5219 [IMT]
Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes [LAAS-ROC]
Language
en
Article de revue
This item was published in
Mathematical Programming. 2020-02
Springer Verlag
English Abstract
In this paper we study the convergence properties of a Nesterov’s family of inertial schemes which is a specific case of inertial Gradient Descent algorithm in the context of a smooth convex minimization problem, under ...Read more >
In this paper we study the convergence properties of a Nesterov’s family of inertial schemes which is a specific case of inertial Gradient Descent algorithm in the context of a smooth convex minimization problem, under some additional hypotheses on the local geometry of the objective function F, such as the growth (or Łojasiewicz) condition. In particular we study the different convergence rates for the objective function and the local variation, depending on these geometric conditions. In this setting we can give optimal convergence rates for this Nesterov scheme. Our analysis shows that there are some situations when Nesterov’s family of inertial schemes is asymptotically less efficient than the gradient descent (e.g. in the case when the objective function is quadratic).Read less <
Origin
Hal imported