Lagrangian Penalty Update

Problem

Take one dual ascent step on the Lagrange multiplier.

Return max(0, lambda + lr * (cost - limit)) so the multiplier grows only while the constraint is violated.

Hint

The projection onto the non-negative orthant keeps the multiplier valid.

case 1

in: [0,2,1,0.5]

expected: 0.5

case 2

in: [1,0,1,0.5]

expected: 0.5

case 3

in: [0.5,1,1,1]

expected: 0.5

case 4

in: [0,0,1,2]

expected: 0

Starter codePython

def lagrangian_penalty_update(lambda_, cost, limit, lr):
    # Your code here
    pass

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