5.4 5.5

学号后四位：“3004”

5.4 求解下列非线性规划：

点击查看代码

import numpy as np  
from scipy.optimize import minimize  
  
def objective(x):  
    return -np.sum(np.sqrt(x) * np.arange(1, 101))  
  
def constraint1(x):  
    return x[1] - 10  
  
def constraint2(x):  
    return 20 - (x[1] + 2*x[2])  
  
def constraint3(x):  
    return 30 - (x[1] + 2*x[2] + 3*x[3])  
  
def constraint4(x):  
    return 40 - (x[1] + 2*x[2] + 3*x[3] + 4*x[4])  
  
def constraint5(x):  
    return 1000 - np.dot(x, np.arange(1, 101))  
  
constraints = [  
    {'type': 'ineq', 'fun': constraint1},  
    {'type': 'ineq', 'fun': constraint2},  
    {'type': 'ineq', 'fun': constraint3},  
    {'type': 'ineq', 'fun': constraint4},  
    {'type': 'ineq', 'fun': constraint5}  
]  
  
bounds = [(0, None)] * 100  
x0 = np.ones(100) * 0.1 
  
result = minimize(objective, x0, method='SLSQP', constraints=constraints, bounds=bounds)  
  
print('Optimal solution:', result.x)  
print('Objective function value at optimal solution:', -result.fun)

print("学号：3004")

5.5 求下列问题的解：

点击查看代码

import numpy as np  
from scipy.optimize import minimize  
  
def objective(x):  
    return 2*x[0] + 3*x[0]**2 + 3*x[1] + x[1]**2 + x[2]  
  
def constraint1(x):  
    return 10 - (x[0] + 2*x[0]**2 + x[1] + 2*x[1]**2 + x[2])  
  
def constraint2(x):  
    return 50 - (x[0] + x[0]**2 + x[1] + x[1]**2 - x[2])  
  
def constraint3(x):  
    return 40 - (2*x[0] + x[0]**2 + 2*x[1] + x[2])  
  

def constraint4(x):  
    return x[0]**2 + x[2] - 2  
  
def constraint5(x):  
    return 1 - (x[0] + 2*x[1])  
  
constraints = [  
    {'type': 'ineq', 'fun': constraint1},  
    {'type': 'ineq', 'fun': constraint2},  
    {'type': 'ineq', 'fun': constraint3},  
    # {'type': 'eq', 'fun': constraint4}, 
    {'type': 'ineq', 'fun': constraint5}  
]  
  

bounds = [(0, None)] * 3  
x0 = np.array([0.1, 0.1, 0.1])  
  
result = minimize(objective, x0, method='SLSQP', constraints=constraints, bounds=bounds)  
  
print('Optimal solution:', result.x)  
print('Objective function value at optimal solution:', result.fun)  

print("学号：3004")