[hal-01073917] Iteration-Complexity of a Generalized Forward Backward Splitting Algorithm

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 ie 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 n0 maximal monotone operators and a co-coercive operator on a Hilbert space The theoretical findings are exemplified with experiments on video processing



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