Design of Fixed Step-Size Distributed Optimization Protocol of Multiagent Systems Over Weighted Unbalanced Digraphs

This paper proposes a novel distributed optimal protocol with a fixed step size for discrete time multi-agent systems to solve a distributed convex optimization problem over a weighted unbalanced digraph. The considered digraph is described by a row stochastic matrix. Each agent with an individual local cost function acquires the state information of in-neighbor agents constantly to update its state estimation. We analyze the existence of the optimal solution and obtain the approximate linear convergence rate through the mean value theorem and the Lyapunov function method. Finally, the validity of the algortthm is verified by the numerical simulation.