A dual-based Distributed Optimization Method on Time-Varying Networks

We propose a time-varying dual accelerated gradient method for minimizing the average of n strongly convex and smooth functions over a time-varying network with n nodes. We prove that the time-varying dual accelerated gradient ascent method converges at a linear rate with the time to reach an ε-neighborhood of the solution being of O(ln 1/ϵ). We test the proposed method on two classes of problems: L_2-regularized least squares and logistic classification problems. For each class, we generate 1000 problems and use the Dolan-Moré performance profiles to compare our obtained results with the ones obtained by several state-of-the-art algorithms to illustrate the efficiency of our method.