Double-Like Accelerated Distributed Optimization Algorithm for Convex Optimization Problem

The optimization problem of minimizing the sum of local convex cost functions on undirected network is studied. Each local convex cost function in the network is accessed only by each node. To be able to get the desired result in an accelerated way, we propose a new double-like accelerated distributed optimization algorithm, named as DA-DOA, to solve the optimization problem over undirected networks. Two momentum terms and gradient tracking are introduced in DA-DOA, and the non-coordinated step-size is adopted at the same time. In the case that the cost function satisfies the general assumptions (smoothness and strong convexity), we prove that DA-DOA can quickly and linearly find the optimal solution of the problem when the step size and momentum coefficient are small enough and positive. Moreover, an explicit linear convergence rate is definitely shown. Finally, Finally, a number of simulation examples verify the validity of DA-DOA and the correctness of the analysis process.