Optimization

"Optimization" here means one specific thing: given a function, find the input that makes its output as small as possible. scipy.optimize does the searching for you, so you don't have to work out the calculus by hand.

Minimizing a function of one variable

minimize_scalar is the simplest entry point — hand it a function that takes a single number and returns a number, and it searches for the input that minimizes the output:

from scipy.optimize import minimize_scalar

def f(x):
    return (x - 3) ** 2 + 5

result = minimize_scalar(f)
print(result.x)
print(result.fun)

3.0
5.0

The function (x - 3)2 + 5 is a parabola with its lowest point at x = 3, where it equals 5 — and that's exactly what minimize_scalar finds, without you ever taking a derivative. result.x is the input that produced the smallest output; result.fun is that smallest output itself.

Minimizing a function of several variables

For a function that takes more than one input, use minimize instead, passing the inputs as a single array-like argument and providing a starting guess with x0:

from scipy.optimize import minimize

def f(point):
    x, y = point
    return (x - 1) ** 2 + (y - 2) ** 2

result = minimize(f, x0=[0, 0])
print(result.x)
print(result.success)

[1. 2.]
True

f is smallest — exactly 0 — at the point (1, 2), and that's what result.x converges to. result.success is worth checking: it's a boolean telling you whether the optimizer actually believes it found a minimum, rather than just giving up.