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We consider an inertial primal-dual algorithm to compute the minimizations ofthe sum of two convex functions and the composition of another convex functionwith a continuous linear operator. With the idea of coordinate descent, wedesign a stochastic coordinate descent inertial primal-dual splittingalgorithm. Moreover, in order to prove the convergence of the proposed inertialalgorithm, we formulate first the inertial version of the randomizedKrasnosel'skii-Mann iterations algorithm for approximating the set of fixedpoints of a nonexpansive operator and investigate its convergence properties.Then the convergence of stochastic coordinate descent inertial primal-dualsplitting algorithm is derived by applying the inertial version of therandomized Krasnosel'skii-Mann iterations to the composition of the proximityoperator.

A stochastic coordinate descent inertial primal-dual algorithm for large-scale composite optimization