The Theory And Application Of Distributed Optimization Algorithm And Game

In this paper,the distributed convex optimization problem is investigated by utilizing the multi-agent systems theory,and a couple of distributed convex optimization algorithms are proposed to compute the optimal solution of the global objection on the network.A distributed optimization algorithm with fixed step size is designed for undirected graph based on the strategies of the gradient tracking and proportional integration,and it has the advantage of speeding up the convergence of the algorithm.For the weighted unbalanced directed graphs,a continuous time distributed optimization algorithm is proposed by tracking the left eigenvector of the Laplacian matrix,extending existing results form undirected graphs to directed graphs.In addition,under weighted unbalanced directed graphs,a distributed dynamic average consensus algorithm is also presented based on consistency.Furthermore,the distributed Nash equilibrium seeking problem is also considered with corresponding distributed algorithms being proposed under unbalanced weighted directed networks.Convergence analysis of the proposed algorithms is analyzed by referring to convex analysis theory and Lyapunov stability theory: the proposed distributed optimization algorithm converges to the optimal solution of the convex optimization problem,the distributed dynamic average consensus algorithm converges to the average value of the inputs,and the distributed game algorithm converges to the Nash equilibrium point.Finally,the effectiveness of the proposed distributed algorithms are verified by four numerical simulations.