admm算法matlab代码

以下是ADMM算法的MATLAB代码示例：

% ADMM algorithm for solving the LASSO problem
% min 1/2*||Ax-b||_2^2 + lambda*||x||_1

% Input:
% A: measurement matrix
% b: measurement vector
% lambda: regularization parameter
% rho: penalty parameter for ADMM
% max_iter: maximum number of iterations
% tol: tolerance for stopping criteria

% Output:
% x: solution of the LASSO problem

function x = admm_lasso(A, b, lambda, rho, max_iter, tol)

% get dimensions of A
[m, n] = size(A);

% initialize variables
x = zeros(n, 1);
z = zeros(n, 1);
u = zeros(n, 1);
Atb = A'*b;
AtA = A'*A;

% ADMM loop
for k = 1:max_iter
    
    % update x
    x = (AtA + rho*eye(n)) \ (Atb + rho*(z - u));
    
    % update z
    zold = z;
    z = soft_threshold(x + u, lambda/rho);
    
    % update u
    u = u + x - z;
    
    % check for convergence
    r = x - z;
    s = rho*(z - zold);
    eps_pri = sqrt(n)*tol + tol*max(norm(x), norm(z));
    eps_dual = sqrt(n)*tol + norm(s);
    if norm(r) < eps_pri && norm(s) < eps_dual
        break;
    end
    
end

end

% soft thresholding operator
function y = soft_threshold(x, lambda)
y = sign(x) .* max(abs(x) - lambda, 0);
end

这是一个简单的示例，可以根据需要进行修改。