一致性ADMM的MATLAB代码

以下是一致性ADMM的MATLAB代码示例：

function [x_global] = consensus_ADMM(x_local, z, rho, neighbors, max_iter, tol)
    for i = 1:max_iter
        x_local_new = local_update(x_local, z, rho);
        received_info = exchange_info(x_local_new, neighbors);
        x_global = sync_variables(x_local_new, received_info);
        z = z + rho * (x_global - x_local_new);
        
        % 判断收敛条件
        if norm(x_local_new - x_local) < tol
            break;
        end
        
        x_local = x_local_new;
    end
end

function [x_local_new] = local_update(x_local, z, rho)
    % 执行局部变量更新
    x_local_new = (z + rho * x_local) / (1 + rho);
end

function [received_info] = exchange_info(x_local, neighbors)
    % 与邻居节点交换信息
    received_info = {};
    for i = 1:numel(neighbors)
        received_info{i} = send_info(neighbors{i}, x_local);
    end
end

function [received_info] = send_info(neighbor, x_local)
    % 模拟发送信息给邻居节点，并返回接收到的信息
    received_info = x_local;
end

function [x_global] = sync_variables(x_local, received_info)
    % 同步变量
    received_info = [x_local; received_info];
    x_global = mean(cell2mat(received_info), 1);
end

% 示例使用，定义一个节点类
classdef Node < handle
    properties
        id
        neighbors
    end
    
    methods
        function self = Node(id)
            self.id = id;
            self.neighbors = {};
        end
        
        function add_neighbor(self, neighbor)
            self.neighbors{end+1} = neighbor;
        end
        
        function received_info = send_info(self, x_local)
            % 模拟发送信息给邻居节点，并返回接收到的信息
            received_info = x_local;
        end
    end
end

% 创建节点
node1 = Node(1);
node2 = Node(2);
node3 = Node(3);

% 设置节点之间的邻居关系
node1.add_neighbor(node2);
node1.add_neighbor(node3);
node2.add_neighbor(node1);
node2.add_neighbor(node3);
node3.add_neighbor(node1);
node3.add_neighbor(node2);

% 初始化参数
x_local = [1, 2, 3];
z = [0, 0, 0];
rho = 0.1;
max_iter = 100;
tol = 1e-4;

% 运行一致性ADMM算法
x_global = consensus_ADMM(x_local, z, rho, {node2, node3}, max_iter, tol);

disp('全局变量：');
disp(x_global);

请注意，上述代码仅提供了一种简单的MATLAB实现示例，实际应用中可能需要根据具体问题进行适当的修改和扩展。