  In the context of convex optimization problems in Hilbert spaces, we induce
inertial effects into the classical ADMM numerical scheme and obtain in this
way so-called inertial ADMM algorithms, the convergence properties of which we
investigate into detail. To this aim we make use of the inertial version of the
Douglas-Rachford splitting method for monotone inclusion problems recently
introduced in [12], in the context of concomitantly solving a convex
minimization problem and its Fenchel dual. The convergence of both sequences of
the generated iterates and of the objective function values is addressed. We
also show how the obtained results can be extended to the treating of convex
minimization problems having as objective a finite sum of convex functions.
