Parallel multi-splitting proximal method for star networks

Ermin Wei

Abstract: We develop a parallel algorithm based on proximal method to solve the problem of minimizing summation of convex (not necessarily smooth) functions over a star network. We show that this method converges to an optimal solution for any choice of constant stepsize for convex objective functions. Under further assumption of Lipschitz-gradient and strong convexity of objective functions, the method converges linearly.