Quadratic error bound of the smoothed gap and the restarted averaged primal-dual hybrid gradient - Laboratoire Traitement et Communication de l'Information Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

Quadratic error bound of the smoothed gap and the restarted averaged primal-dual hybrid gradient

Résumé

We study the linear convergence of the primal-dual hybrid gradient method. After a review of current analyses, we show that they do not explain properly the behavior of the algorithm, even on the most simple problems. We thus introduce the quadratic error bound of the smoothed gap, a new regularity assumption that holds for a wide class of optimization problems. Equipped with this tool, we manage to prove tighter convergence rates. Then, we show that averaging and restarting the primal-dual hybrid gradient allows us to leverage better the regularity constant. Numerical experiments on linear and quadratic programs, ridge regression and image denoising illustrate the findings of the paper.
Fichier principal
Vignette du fichier
new_regularity_and_rapdhg.pdf (594.52 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03228252 , version 1 (18-05-2021)
hal-03228252 , version 2 (03-06-2022)
hal-03228252 , version 3 (13-04-2023)

Identifiants

  • HAL Id : hal-03228252 , version 1

Citer

Olivier Fercoq. Quadratic error bound of the smoothed gap and the restarted averaged primal-dual hybrid gradient. 2021. ⟨hal-03228252v1⟩
411 Consultations
230 Téléchargements

Partager

Gmail Facebook X LinkedIn More