BFGS Scalar Inverse Hessian Update

Problem

In one dimension the BFGS inverse Hessian update reduces to H_new = s / y with s = x_new - x_old and y = g_new - g_old; return the previous H when y is zero.

Given s, y, and the previous inverse Hessian h0, return the updated value.

Hint

The curvature condition y > 0 keeps the estimate positive.

Test cases

case 1

in: [1,2,1]

expected: 0.5

case 2

in: [0.5,0,3]

expected: 3

case 3

in: [-0.25,-0.5,2]

expected: 0.5

Starter codePython

def bfgs_scalar_inverse_hessian_update(s, y, h0):
    # Your code here
    pass

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