Heavy Ball Stability Check

Problem

Check the stability of heavy-ball momentum on a quadratic with curvature L.

The iteration converges when lr > 0, 0 <= mu < 1, and lr * L < 2 * (1 + mu) all hold. Return True only when every condition is satisfied.

Hint

Higher momentum buys a slightly larger stable step size.

case 1

in: [0.1,1,0.9]

expected: true

case 2

in: [0.5,1,0]

expected: true

case 3

in: [2.5,1,0.5]

expected: true

case 4

in: [1,1,1]

expected: false

case 5

in: [-0.1,1,0.5]

expected: false

Starter codePython

def heavy_ball_stable(lr, L, mu):
    # Your code here
    pass

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