  We consider an inertial primal-dual algorithm to compute the minimizations of
the sum of two convex functions and the composition of another convex function
with a continuous linear operator. With the idea of coordinate descent, we
design a stochastic coordinate descent inertial primal-dual splitting
algorithm. Moreover, in order to prove the convergence of the proposed inertial
algorithm, we formulate first the inertial version of the randomized
Krasnosel'skii-Mann iterations algorithm for approximating the set of fixed
points of a nonexpansive operator and investigate its convergence properties.
Then the convergence of stochastic coordinate descent inertial primal-dual
splitting algorithm is derived by applying the inertial version of the
randomized Krasnosel'skii-Mann iterations to the composition of the proximity
operator.
