Gradient Lipschitz Constant

Problem

For the quadratic f(x, y) = 0.5*(a*x^2 + 2*b*x*y + c*y^2), the gradient is Lipschitz with constant equal to the largest eigenvalue of the Hessian [[a, b], [b, c]].

That eigenvalue is (a + c)/2 + sqrt(((a - c)/2)^2 + b^2). Given a, b, c, return the constant.

Hint

The gradient of a quadratic is a linear map, so its Lipschitz constant is the spectral norm.

Test cases

case 1

in: [4,0,1]

expected: 4

case 2

in: [2,1,2]

expected: 3

case 3

in: [1,0,1]

expected: 1

case 4

in: [5,0,3]

expected: 5

Starter codePython

def gradient_lipschitz(a, b, c):
    # Your code here
    pass

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