5.5习题

5.5

代码：

import numpy as np  
from scipy.optimize import minimize   
def objective(x):  
    x1, x2, x3 = x  
    return -(2*x1 + 3*x1**2 + 3*x2 + x2**2 + x3)   
constraints = [  
    {'type': 'ineq', 'fun': lambda x: 10 - (x[0] + 2*x[0]**2 + x[1] + 2*x[1]**2 + x[2])},  
    {'type': 'ineq', 'fun': lambda x: 50 - (x[0] + x[0]**2 + x[1] + x[1]**2 - x[2])},     
    {'type': 'ineq', 'fun': lambda x: 40 - (2*x[0] + x[0]**2 + 2*x[1] + x[2])},           
    {'type': 'eq',   'fun': lambda x: 2 - (x[0]**2 + x[2])},                              
    {'type': 'ineq', 'fun': lambda x: x[0] + 2*x[1] - 1}                                
]  
bounds = [(0, None), (None, None), (None, None)]
x0 = [0, 0, 0]   
result = minimize(objective, x0, bounds=bounds, constraints=constraints)    
if result.success:  
    print("Optimal solution found:")  
    print("x1 =", result.x[0])  
    print("x2 =", result.x[1])  
    print("x3 =", result.x[2])  
    print("Maximum f(x) =", -result.fun)  
else:  
    print("Optimization failed.") 

结果：

Optimal solution found:
x1 = 2.3333333314551923
x2 = 0.1666666730500357
x3 = -3.4444444356792134
Maximum f(x) = 18.083333333326205