This talk presents the convergence rate analysis for the inexact Krasnosel'skii-Mann iteration built from nonexpansive operators.
The presented results include two main parts: global pointwise/ergodic iteration-complexity bounds, and local linear convergence under a metric subregularity assumption. Some monotone operator splitting methods, to which the presented iteration-complexity bounds can be applied to, are discussed. These methods include the (Generalized) Forward-Backward, Douglas-Rachford, ADMM and several Primal-Dual splitting methods. The usefulness of the results is illustrated by applying them to a large class of composite convex optimization problems arised from signal/image processing problems.