ADMM One Step 1D

Problem

Perform one ADMM iteration minimizing 0.5 * (x - a_val) ** 2 + lam * abs(z) subject to x - z = 0, with scaled dual u and penalty rho.

Set x to (a_val + rho * (z - u)) / (1 + rho), set z by soft-thresholding x + u at lam / rho, then set u = u + x - z. Return [x, z, u].

Hint

The z update is soft thresholding of x + u at lam / rho.

case 1

in: [0,0,0,3,0.5,1]

expected: [1.5,1,0.5]

case 2

in: [1,0,0,2,0.1,2]

expected: [0.6666666666666666,0.6166666666666666,0.050000000000000044]

case 3

in: [0,0.5,0.2,-1,1,0.5]

expected: [-0.5666666666666667,0,-0.36666666666666664]

Starter codePython

def admm_step(x, z, u, a_val, lam, rho):
    # Returns [x, z, u]
    # Your code here
    pass

3 test cases · run your code against them in the editor