# %% Import:

import numpy as np

# %% Def of objective function:

def fun_f(x1, x2):
    f = (x1 - 1)**2 + (x2 - 2)**2 + 0.5
    return f

# %% Initialization:

x1_lb = 0
x1_ub = 2
N_x1 = 100
x1_array = np.linspace(x1_lb, x1_ub, N_x1)

x2_lb = 1
x2_ub = 3
N_x2 = 100
x2_array = np.linspace(x2_lb, x2_ub, N_x2)

f_min = np.inf
x1_opt = 0
x2_opt = 0

# %% Grid optim:

for x1 in x1_array:

    for x2 in x2_array:

        # Calulation of objective function:
        f = fun_f(x1, x2)  

        # Improvement of solution:
        if (f < f_min):
            f_min = f
            x1_opt = x1
            x2_opt = x2

# %% Displaying results:

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