A stochastic coordinate descent primal-dual algorithm with dynamic   stepsize for large-scale composite optimization
  In this paper we consider the problem of finding 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 primal-dual splitting algorithm with dynamic stepsize. Based on randomized Modified Krasnosel'skii-Mann iterations and the firmly nonexpansive properties of the proximity operator, we achieve the convergence of the proposed algorithms. Moreover, we give two applications of our method. 
Meng Wen, Shigang Yue, Yuchao Tang, Jigen Peng
math.OC