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Local Linear Convergence of Inertial Forward-Backward Splitting for Low Complexity Regularization

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sparsifbrate.pdf (291.6Kb)
Date
2015
Dewey
Traitement du signal
Sujet
Forward-Backward Splitting
Conference name
SPARS
Conference date
2015
Conference city
Cambridge
Conference country
United Kingdom
URI
https://basepub.dauphine.fr/handle/123456789/20862
Collections
  • CEREMADE : Publications
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Author
Liang, Jingwei
150 Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen [GREYC]
Fadili, Jalal M.
150 Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen [GREYC]
Peyré, Gabriel
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Communication / Conférence
Abstract (EN)
In this abstract, we consider the inertial Forward-Backward (iFB) splitting method and its special cases (Forward-Backward/ISTA and FISTA). Under the assumption that the non-smooth part of the objective is partly smooth relative to an active smooth manifold, we show that iFB-type methods (i) identify the active manifold in finite time, then (ii) enter a local linear convergence regime that we characterize precisely. This gives a grounded and unified explanation to the typical behaviour that has been observed numerically for many low-complexity regularizers, including 1 , 1,2-norms, total variation (TV) and nuclear norm to name a few. The obtained results are illustrated by concrete examples.

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