ADMM Residual Norms

Problem

Compute the primal and dual residuals of an ADMM step.

Return [primal, dual] where primal = ||x - z|| and dual = rho * ||z - z_prev||. These are the standard quantities compared against tolerances for stopping.

Hint

The dual residual measures how much z changed from the previous iteration.

Test cases

case 1

in: [[1,2],[0.5,1.5],[0,1],1]

expected: [0.7071067811865476,0.7071067811865476]

case 2

in: [[0,0,0],[0,0,0],[0,0,0],2]

expected: [0,0]

case 3

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

expected: [0,0.3535533905932738]

Starter codePython

def admm_residual_norms(x, z, z_prev, rho):
    # Returns [primal, dual]
    # Your code here
    pass

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