Convexity Check Quadratic

Problem

Check whether a 2x2 quadratic has a positive semidefinite Hessian.

With A = [[a, b], [c, d]], symmetrize b = (b + c) / 2 and return True only when a >= 0, d >= 0, and a * d - b ** 2 >= 0. These are the Sylvester conditions for convexity.

Hint

A symmetric 2x2 matrix is PSD when its diagonal is non-negative and its determinant is non-negative.

Test cases

case 1

in: [[[2,1],[1,2]]]

expected: true

case 2

in: [[[2,3],[3,2]]]

expected: false

case 3

in: [[[0,1],[1,0]]]

expected: false

case 4

in: [[[1,0],[0,0]]]

expected: true

Starter codePython

def is_convex_quadratic(A):
    # Your code here
    pass

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