MediumCalculusca-072

Convexity Check via Hessian

Problem

A twice-differentiable function of two variables is convex when its Hessian is positive semidefinite everywhere.

For the constant Hessian H = [[p, q], [q, r]], this holds exactly when p >= 0, r >= 0, and p*r - q^2 >= 0. Return a boolean.

Hint

Sylvester's criterion for a 2x2 symmetric matrix: all leading principal minors are nonnegative.

case 1

in: [2,0,2]

expected: true

case 2

in: [2,3,2]

expected: false

case 3

in: [0,0,0]

expected: true

case 4

in: [1,1,1]

expected: true

case 5

in: [-1,0,1]

expected: false

Starter codePython

def is_convex_hessian(p, q, r):
    # Return True if H is positive semidefinite
    # Your code here
    pass

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