pyth

import numpy as np
import plotly.graph_objs as go
from scipy.optimize import minimize

def f(x):
    x1, x2 = x
    return x1**2 - 5*x1 + 2*x2**2 - x2 - x1*x2

def constraint1(x):
    return x[0]

def constraint2(x):
    return x[1]

def constraint3(x):
    return 5 - x[0] - x[1]

constraint_1 = {'type': 'ineq', 'fun': constraint1}
constraint_2 = {'type': 'ineq', 'fun': constraint2}
constraint_3 = {'type': 'ineq', 'fun': constraint3}
constraints = [constraint_1, constraint_2, constraint_3]

result = minimize(f, [0, 0], constraints=constraints)
minimum = result.x  # Współrzędne punktu minimalnego

x = np.linspace(-2, 6, 400)
y = np.linspace(-2, 6, 400)
X, Y = np.meshgrid(x, y)
Z = f([X, Y])

fig = go.Figure(data=go.Contour(x=x, y=y, z=Z, colorscale='spectral', opacity=0.8))
fig.update_layout(xaxis_title='x1', yaxis_title='x2', title='Funkcja f(x1,x2) z ograniczeniami')

x_constraint = np.linspace(0, 5, 100)
y_constraint = 5 - x_constraint
fig.add_trace(go.Scatter(x=x_constraint, y=y_constraint, mode='lines', fill='tozeroy', fillcolor='rgba(4, 7241, 12, 0.5)', line=dict(color='black', width=3, dash='dash'), name='x1 + x2 >= 5'))
fig.add_annotation(x=3, y=2, text="x1 + x2 >= 5", showarrow=False, font=dict(color='white', size=15))

x_line = np.linspace(-2, 6, 10)
y_line = np.zeros_like(x_line)
fig.add_trace(go.Scatter(x=x_line, y=y_line, mode='lines', line=dict(color='black', width=3, dash='dash'), name='x1 >= 0'))
fig.add_annotation(x=6, y=0.5, text="x1 >= 0", showarrow=False, font=dict(color='white', size=15))

y_line = np.linspace(-2, 6, 10)
x_line = np.zeros_like(y_line)
fig.add_trace(go.Scatter(x=x_line, y=y_line, mode='lines', line=dict(color='black', width=3, dash='dash'), name='x2 >= 0'))
fig.add_annotation(x=0.5, y=6, text="x2 >= 0", showarrow=False, font=dict(color='white', size=15))

fig.add_trace(go.Scatter(x=[minimum[0]], y=[minimum[1]], mode='markers', marker=dict(color='blue', size=10), name='Minimum'))
fig.add_trace(go.Scatter(x=[29/8], y=[11/8], mode='markers', marker=dict(color='yellow', size=10), name='Minimum globalne'))

fig.update_layout(legend=dict(x=1.2, y=1), # Ustawienie legendy z prawej strony
                  xaxis_title='x1', yaxis_title='x2', title='Funkcja f(x1,x2) z ograniczeniami')
fig.show()