OPTIMAL CONVERGENCE RATES FOR NESTEROV ACCELERATION

Abstract : In this paper, we study the behavior of solutions of the ODE associated to Nesterov acceleration. It is well-known since the pioneering work of Nesterov that the rate of convergence O(t 2) is optimal for the class of convex functions. In this work, we show that better convergence rates can be obtained with some additional geometrical conditions, such as Lojasiewicz property. More precisely, we prove the optimal convergence rates that can be obtained depending on the geometry of the function F to minimize. The convergence rates are new, and they shed new light on the behavior of Nesterov acceleration schemes.
Type de document :
Pré-publication, Document de travail
Rapport LAAS n° 18120. 2018
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https://hal.archives-ouvertes.fr/hal-01786117
Contributeur : Aude Rondepierre <>
Soumis le : lundi 14 mai 2018 - 11:49:21
Dernière modification le : mercredi 23 mai 2018 - 17:58:04

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  • HAL Id : hal-01786117, version 2
  • ARXIV : 1805.05719

Citation

Jean François Aujol, Charles Dossal, Aude Rondepierre. OPTIMAL CONVERGENCE RATES FOR NESTEROV ACCELERATION. Rapport LAAS n° 18120. 2018. 〈hal-01786117v2〉

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