https://stackoverflow.com/a/48866951/2320035

1d_gridsearch_polishing_example.py

import numpy as np
from scipy.optimize import minimize_scalar, minimize
import matplotlib.pyplot as plt

""" EXAMPLE PROB """

N_EVAL = 5
N_BOUNDS = (0., 1.2)
grid1d = np.linspace(*N_BOUNDS, N_EVAL)

def fun(x):
    return -(1.4 - 3*x) * np.sin(18*x)

""" MANUAL (NON-)GRID-SEARCH WITH POLISHING """
raw_funs, polished_x, polished_funs = [], [], []
for x in grid1d:
    fun_eval = fun(x)
    raw_funs.append(fun_eval)

    # use multivariate-opt as 1d-opt finds global-opt too easily!
    # (want to show local-opt!)
    polished_res = minimize(fun, x, method='L-BFGS-B', bounds=[N_BOUNDS])
    polished_x.append(polished_res.x)
    polished_funs.append(polished_res.fun)

""" PLOT """
plot_x = np.linspace(*N_BOUNDS, 100)
plot_y = fun(plot_x)
ax = plt.subplot(111)

ax.plot(plot_x, plot_y, color='black')

[ax.axvline(i, color='blue') for i in grid1d]

ax.scatter(grid1d, raw_funs, color='blue', label='raw grid-eval')
ax.scatter(polished_x, polished_funs, color='red', label='polished by local-opt')

# ugly code
for i in range(N_EVAL):
    ax.arrow(grid1d[i], raw_funs[i],
             (polished_x[i]-grid1d[i])[0],
             (polished_funs[i]-raw_funs[i])[0],
             color='magenta')

plt.legend(loc=2)
plt.show()