5.4 5.5

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")