auto_math_constraints_duality_and_shadow_prices_5

Snippet from Math-Constraints-Duality-and-Shadow-Prices.md

def plot_constraint_landscape(A, b, x_history, constraint_names):
    """2D constraint view."""
    fig, ax = plt.subplots(figsize=(10, 8))
    
    for i, name in enumerate(constraint_names):
        if A.shape[1] == 2:
            x_line = np.linspace(0, b[i] / A[i, 0], 100)
            y_line = (b[i] - A[i, 0] * x_line) / A[i, 1]
            ax.plot(x_line, y_line, label=f'{name}', linewidth=2 if i==0 else 1)
    
    x_hist = np.array(x_history)
    ax.plot(x_hist[:, 0], x_hist[:, 1], 'ko-', alpha=0.5, label='Path')
    ax.plot(x_hist[-1, 0], x_hist[-1, 1], 'r*', markersize=15, label='Optimum')
    
    ax.set_xlabel('Dim 1')
    ax.set_ylabel('Dim 2')
    ax.legend()
    ax.grid(alpha=0.3)
    plt.title('Constraints with Path')
    plt.savefig('landscape.png', dpi=150)
    print("Saved to landscape.png")
    
# Example
plot_constraint_landscape(A, b, [x0, x_feas, x_opt], ['Cost', 'Time'])