Subgradient Step For Absolute Value

Problem

Minimize f(x) = |x| with the subgradient method.

For n_iters iterations use g = 1 if x > 0, g = -1 if x < 0, and g = 0 when x is exactly 0, then update x = x - lr * g. Return the final value of x.

Hint

Once x reaches 0 the chosen subgradient is 0, so it stays there.

case 1

in: [3,0.5,10]

expected: 0

case 2

in: [-2.5,0.5,4]

expected: -0.5

case 3

in: [0.2,0.1,3]

expected: 0

case 4

in: [0,0.1,5]

expected: 0

Starter codePython

def subgradient_step_abs(x, lr, n_iters):
    # Minimize f(x) = |x|
    # Your code here
    pass

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