  For composite nonsmooth optimization problems, Forward-Backward algorithm
achieves model identification (e.g. support identification for the Lasso) after
a finite number of iterations, provided the objective function is regular
enough. Results concerning coordinate descent are scarcer and model
identification has only been shown for specific estimators, the support-vector
machine for instance. In this work, we show that cyclic coordinate descent
achieves model identification in finite time for a wide class of functions. In
addition, we prove explicit local linear convergence rates for coordinate
descent. Extensive experiments on various estimators and on real datasets
demonstrate that these rates match well empirical results.
