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SUMMARY:A generalized Forward-Backward splitting for sums of maximal monot
 one operators: application to sparsity-­&#8208\;regularized inverse probl
 ems
DTSTART:20110621T140000
DTSTAMP:20260506T132921Z
UID:e34d2c28c64b7c22dc894b53a6b06f65057b4b2e07357eb617bda743
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Jalal Fadili\, GREYC CNRS\nSplitting methods for maximal
  monotone operators have numerous applications in constructing decompositi
 on algorithms for convex optimization and monotone variational inequalitie
 s. Splitting algorithms have an old extensive literature\, but have been p
 opularized in the signal/image processing community only recently for solv
 ing a wide range of inverse problems. In this work\, we describe a general
  algorithm for finding a zero of the sum of n+1 maximal monotone operators
  over a real Hilbert space\, where one of the operators is single- valued.
  Our splitting scheme encompasses the classical forward-backward splitting
  for n=1\, as well as the Douglas-Rachford splitting (and its extension). 
 We provide a detailed convergence analysis and establish stability to erro
 rs of the proposed iteration. The framework is then applied to the minimiz
 ation of the composite objective function F(x)+sum_i G_i(x)\, where all fu
 nctions are proper lower- semicontinuous and convex\, and F is differentia
 ble with a Lipschitz-continuous gradient. Many important inverse problems 
 amount to minimizing such functions\, e.g. mixed regularization\, structur
 ed sparsity\, etc.. We then describe several experiments and report compar
 ison to other algorithms to demonstrate the potential applicability of our
  approach.
LOCATION:SG 0211 https://plan.epfl.ch/?room==SG%0200211
STATUS:CONFIRMED
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