Convex Conjugate of exp

Problem

Return the convex conjugate of f(x) = exp(x):

f*(y) = sup_x (x * y - exp(x)) = y * ln(y) - y for y > 0

and 0 at y = 0.

Hint

The conjugate of the exponential is the negative entropy of a Poisson-like variable.

case 1

in: [1]

expected: -1

case 2

in: [2]

expected: -0.6137056388801094

case 3

in: [0.5]

expected: -0.8465735902799727

case 4

in: [0]

expected: 0

Starter codePython

import math
def convex_conjugate_exp(y):
    # Your code here
    pass

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