Understanding the error for scipy.optimize.minimize() function

Question

I have a simple equation that I plotted via

def chernoff_bound(beta):
    return 0.5 * np.exp(-beta * (1-beta))

betas = np.arange(0, 1, 0.01)
c_bound = cher         


        

Answer 1

The second argument of optimize.minimize is an initial guess -- your guess for the minimum x-value that you wish optimize.minimize to find. So, for example,

import numpy as np
from scipy import optimize
x0 = 0.1
fun = lambda x: 0.5 * np.exp(-x * (1-x))
res = optimize.minimize(fun, x0, method='Nelder-Mead')
print(res)

yields

  status: 0
    nfev: 36
 success: True
     fun: 0.38940039153570244
       x: array([ 0.5])
 message: 'Optimization terminated successfully.'
     nit: 18

x0 need not always be a scalar. It could be an array -- it depends on fun. In the above example, x0 = np.array([0.1]) would also work. The key point is that for whatever you guess, fun(x0) should be a scalar.