1.5.12.1. Finding the minimum of a smooth function

Demos various methods to find the minimum of a function.

import numpy as np
import matplotlib.pyplot as plt


def f(x):
    return x**2 + 10 * np.sin(x)


x = np.arange(-5, 5, 0.1)
plt.plot(x, f(x))

[<matplotlib.lines.Line2D object at 0x7f791f2890d0>]

Now find the minimum with a few methods

import scipy as sp

# The default (Nelder Mead)
print(sp.optimize.minimize(f, x0=0))

 message: Optimization terminated successfully.
 success: True
  status: 0
     fun: -7.945823375615215
       x: [-1.306e+00]
     nit: 5
     jac: [-1.192e-06]
hess_inv: [[ 8.589e-02]]
    nfev: 12
    njev: 6

plt.show()