# %% Import:

import numpy as np

# %% Def of objective function:

def fun_f(x1, x2):
    f = (x1 - 1)**2 + (x2 - 2)**2 + 0.5
    # Constraint:
    if not(x2 - x1 - 1.5 >= 0):
        f = np.inf
    return f

# %% Optimal solution:

x1_opt = 0.74747475
x2_opt = 2.25252525
f_min = fun_f(x1_opt, x2_opt)

print('-----------------')
print(f'x1_opt = {x1_opt:.8f}')
print(f'x2_opt = {x2_opt:.8f}')
print(f'f_min = {f_min:.8f}')

# %% Perturbation of optim variables:

kx1 = 0.99
kx2 = 1.00

x1_pert = x1_opt * kx1
x2_pert = x2_opt * kx2
f_pert = fun_f(x1_pert, x2_pert)
df = f_pert - f_min

print('-----------------')
print(f'x1_pert = x1_opt*{kx1:.2f}')
print(f'x2_pert = x2_opt*{kx2:.2f}')
print(f'f_pert - f_min = {df:.8f}')
print('-----------------')
print('Test ok?', (df > 0))