A Generalized Forward-Backward Splitting

An algorithmic scheme for solving, over any real Hilbert space ℋ, monotone inclusion problems of the form
find x ∈ zer (i=1n Ai + B ) , where:

In particular, it enables minimization over ℋ of convex problems of the form
find x∈ argmin i=1n gi + f , where:

Work done in collaboration with Jalal Fadili and Gabriel Peyré.
Published in SIAM Journal of Imaging Sciences: Permalink - Author's manuscript - reference as BibTeX format.
Erratum: on top of page 10 (1208 in the volume), in the application of the Sherman–Morrison–Woodbury formula in equation (3.3), a factor γ has been forgotten.
Source code of numerical simulations used in the paper is not maintained anymore, feel free to contact me for any question.

A more complete version of this work can be found in chapters III and IV of my Ph.D. thesis.
See also the preconditioned version, or the forward-Douglas–Rachford version.

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