Distributed optimization for multi-agent system over unbalanced graphs with linear convergence rate

Abstract

Distributed optimization over unbalanced graphs is an important problem in multi-agent systems.Most of literatures, by introducing some auxiliary variables, utilize the Push-Sum scheme to handle the widespread unbalance graph with row or column stochastic matrix only.But the introduced auxiliary dynamics bring more calculation and communication tasks.In this paper, based on the in-degree and out-degree information of each agent, we propose an innovative distributed optimization algorithm to reduce the calculation and communication complexity of the conventional Push-Sum scheme.Furthermore, with the aid of small gain theory, we prove the linear convergence rate of the proposed algorithm.