MediumCalculusca-216

Conjugate Function Value

Problem

The convex conjugate of f(x) = e^x is f*(y) = y * log(y) - y for y > 0, with f*(0) = 0.

Given y >= 0, return f*(y). The conjugate is always convex in y.

Hint

Maximize y*x - e^x over x; the optimizer is x = log(y).

case 1

in: [1]

expected: -1

case 2

in: [0]

expected: 0

case 3

in: [2]

expected: -0.6137056388801094

case 4

in: [0.5]

expected: -0.8465735902799727

case 5

in: [2.718281828459045]

expected: 0

Starter codePython

def conjugate_exp(y):
    # Your code here
    pass

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