
Iteration-Complexity of a Generalized Forward Backward Splitting Algorithm
Liang, Jingwei; Fadili, Jalal; Peyré, Gabriel (2014), Iteration-Complexity of a Generalized Forward Backward Splitting Algorithm, ICASSP 2014, 2014-04, Florence, Italie
View/ Open
Type
Communication / ConférenceExternal document link
https://hal.archives-ouvertes.fr/hal-01073917Date
2014Conference title
ICASSP 2014Conference date
2014-04Conference city
FlorenceConference country
ItaliePages
6
Metadata
Show full item recordAuthor(s)
Liang, JingweiGroupe de Recherche en Informatique, Image et Instrumentation de Caen [GREYC]
Fadili, Jalal
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Peyré, Gabriel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this paper, we analyze the iteration-complexity of Generalized Forward-Backward (GFB) splitting algorithm, as proposed in [2], for minimizing a large class of composite objectives on a Hilbert space, where f has a Lipschitz-continuous gradient and the hi's are simple (i.e. their proximity operators are easy to compute). We derive iteration-complexity bounds (pointwise and ergodic) for the inexact version of GFB to obtain an approximate solution based on an easily verifiable termination criterion. Along the way, we prove complexity bounds for relaxed and inexact fixed point iterations built from composition of nonexpansive averaged operators. These results apply more generally to GFB when used to find a zero of a sum of n>0 maximal monotone operators and a co-coercive operator on a Hilbert space. The theoretical findings are exemplified with experiments on video processing.Subjects / Keywords
Convex optimization; Proximal splitting; Convergence rates; Inverse problemsRelated items
Showing items related by title and author.
-
Liang, Jingwei; Fadili, Jalal M.; Peyré, Gabriel (2015) Communication / Conférence
-
Liang, Jingwei; Fadili, Jalal; Peyré, Gabriel (2014) Communication / Conférence
-
Liang, Jingwei; Fadili, Jalal; Peyré, Gabriel (2014) Communication / Conférence
-
Peyré, Gabriel; Fadili, Jalal; Raguet, Hugo (2013) Article accepté pour publication ou publié
-
Liang, Jingwei; Fadili, Jalal; Peyré, Gabriel (2018) Article accepté pour publication ou publié