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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

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Type
Communication / Conférence
External document link
https://hal.archives-ouvertes.fr/hal-01073917
Date
2014
Conference title
ICASSP 2014
Conference date
2014-04
Conference city
Florence
Conference country
Italie
Pages
6
Metadata
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Author(s)
Liang, Jingwei
Groupe 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 problems

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