我正在尝试使用Scipy的minimize函数解决一个最小化问题。目标函数简单地是两个具有不同均值和方差的多元正态分布的比率。我希望找到函数g_func的最大值,这等价于找到函数g_optimization的最小值。此外,我添加了一个约束条件x[0] = 0。这里,x是一个包含8个元素的向量。目标函数g_optimization如下所示:
优化在两次迭代后停止,函数给出的最小值为0,在点np.array([0,10.32837891,-1.62396508,10.13790152,12.38752653,9.11615259,3.53201544,-4.22115517])。这是不可能的,因为即使我们将起始点np.zeros(8)输入g_optimization函数,得到的结果也是-657.0041125829354,比0更小。所以提供的解决方案绝对不是最小值。
我不确定我哪里做错了。
import numpy as np
from scipy.optimize import minimize
# Set up mean and variance for two MVN distributions
n_trait = 8
sigma = np.full((n_trait, n_trait),0.0005)
np.fill_diagonal(sigma,0.005)
omega = np.full((n_trait, n_trait),0.0000236)
np.fill_diagonal(omega,0.0486)
sigma_pos = np.linalg.inv(np.linalg.inv(sigma)+np.linalg.inv(omega))
mu_pos = np.array([-0.01288244,0.08732091,0.01049617,0.0860966,0.10055626,0.07952922,0.04363669,-0.0061975])
mu_pri = 0
sigma_pri = omega
#objective function
def g_func(beta,mu_sim_pos):
g1 = ((np.linalg.det(sigma_pri))**(1/2))/((np.linalg.det(sigma_pos))**(1/2))
g2 = (-1/2)*np.linalg.multi_dot([np.transpose(beta-mu_sim_pos),np.linalg.inv(sigma_pos),beta-mu_sim_pos])
g3 = (1/2)*np.linalg.multi_dot([np.transpose(beta-mu_pri),np.linalg.inv(sigma_pri),beta-mu_pri])
g = g1*np.exp(g2+g3)
return g
def g_optimization(beta,mu_sim_pos):
return -1*g_func(beta,mu_sim_pos)
#optimization
start_point = np.full(8,0)
cons = ({'type': 'eq',
'fun' : lambda x: np.array([x[0]])})
anws = minimize (g_optimization, [start_point], args=(mu_pos),
constraints=cons, options={'maxiter': 50}, tol=0.001)
anws
优化在两次迭代后停止,函数给出的最小值为0,在点np.array([0,10.32837891,-1.62396508,10.13790152,12.38752653,9.11615259,3.53201544,-4.22115517])。这是不可能的,因为即使我们将起始点np.zeros(8)输入g_optimization函数,得到的结果也是-657.0041125829354,比0更小。所以提供的解决方案绝对不是最小值。
g_optimization(np.zeros(8),mu_pos) #gives solution of -657.0041125829354
我不确定我哪里做错了。