A stochastic coordinate descent primal-dual algorithm and applications

First, we introduce a splitting algorithm to minimize a sum of three convex functions. The algorithm is of primal dual kind and is inspired by recent results of Vũ and Condat. Second, we provide a randomized version of the algorithm based on the idea of coordinate descent. Finally, we address two applications of our method: (i) for stochastic minibatch optimization; and (ii) for distributed optimization.