Accelerated Distributed Optimization over Directed Graphs with Row and Column-Stochastic Matrices

Abstract

In this paper, we study distributed optimization problem over multi-agent networks where the goal is to find the global optimal of a sum of convex functions over strongly connected and directed graphs. A novel distributed algorithm is proposed where both row and column-stochastic matrices are utilized to bypass the limits of the implementation of doubly-stochastic matrices or eigenvector estimation in related work. Besides, it has an evident expression and accelerated convergence by introducing the momentum term. Combining the Generalized Small Gain Theorem with Linear Time Invariant (LTI) system inequality, the algorithm is proved to be able to linearly converge to the exact optimal solution. Furthermore, the ranges of stepsize and momentum paramater are characterized, respectively. Finally, simulation results illustrate effectiveness of the method and correctness of theoretical analysis.