  In this paper, we propose a randomized intertial block-coordinate primaldual
fixed point algorithm to solve a wide array of monotone inclusion problems base
on the modification of the heavy ball method of Nesterov. These methods rely on
a sweep of blocks of variables which are activated at each iteration according
to a random rule. To this end we formulate the inertial version of the
Krasnosel'skii-Mann algorithm for approximating the set of fixed points of a
quasinonexpansive operator, for which we also provide an exhaustive convergence
analysis. As a by-product, we can obtain some intertial block-coordinate
operator splitting methods for solving composite monotone inclusion and convex
minimization problems.
