Abstract : Various recent iterative optimization methods require to compute the proximity operator of a sum of functions.
We address this problem by proposing a new distributed algorithm for a sum of non-necessarily smooth convex functions
composed with arbitrary linear operators. In our approach, each function is associated with a node of a graph, which
communicates with its neighbors. Our algorithm relies on a primal-dual splitting strategy that avoids to invert any linear
operator, thus making it suitable for processing high-dimensional datasets. The proposed algorithm has a wide array of applications
in signal/image processing and machine learning and its convergence is established.