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On convergence rate of Accelerated Dual Descent Algorithm

We expand and refine the convergence rate analysis of the Accelerated Dual Descent (ADD) Algorithm, a fast distributed solution to the convex network flow optimization problem. ADD uses local information to compute an approximate Newton direction for the dual problem. It has been previously shown that the quality of the approximation depends on a network invariant related to the expansion properties of the underlying graph. The main result of this work is to characterize this information spreading parameter in terms of the network structure and properties of the primal objective. The three phase convergence Theorem for ADD is revisited and bounds which explicitly depend on the network structure are presented. Additionally, an upper bound on the number of iterations required to reach the terminal phase is proven. We explore what type of graphs work best with ADD by examining our characterization of the information spreading coefficient in the context of commonly studied network structures.