Theory And Application Of Distributed Optimization Based On Multi-agent Systems

Recently,distributed optimization problems based on multi-agent systems have attracted extensive attention.For distributed optimization problems,the algorithms design and the convergence analysis are the key points.Therefore,this paper is devoted to the study of distributed second-order optimization algorithm and its convergence analysis to solve the distributed unconstrained convex optimization problem.This paper first considers the distributed unconstrained convex optimization problem over undirected graph,and proposes a novel continuous-time distributed second-order optimization algorithm based on the constant step-size scheme and the gradient tracking strategy.The proposed algorithm aims to abandon the use of diminishing step-sizes scheme,accelerate the convergence rate of the distributed first-order optimization algorithm and further extend the distributed second-order optimization algorithms in the existing literature.In addition,this paper considers the communication cost problem caused by the excessive variables communicated in undirected multi-agent network system.By reducing the variable of information communication in the network,this paper modifies and proposes a distributed second-order algorithm with communication-alleviation based on the original distributed second-order optimization algorithm.The proposed communicationalleviation algorithm can reduce the communication cost and improve the communication efficiency of the original algorithm.This paper also considers the distributed unconstrained convex optimization problem over unbalanced directed graph,and generalizes the original distributed second-order optimization algorithm from an undirected graph to an unbalanced directed graph,and extends the existing second-order algorithms that are mainly applied to the cases of undirected or balanced directed graphs.Finally,three numerical simulation examples are presented to verify the effectiveness and the convergence performances of the proposed algorithms.