更新函数并从 scipy 获取迭代结果

Question

def f(params):

    pi12, pi21 = params

    LL = 10*np.log(40*60/110**2) + 30*np.log(40*50/110**2) + 20*np.log(20/110*(50/110 + 60/110*pi12)) + \ 

         50*np.log(50/110*(60/110 + 50/110*pi21)) - 110*np.log(40*60/110**2 + 40*50/110**2 + \

         20/110*(50/110 + 60/110*pi12) + 50/110*(60/110 + 50/110*pi21))

    return -LL

def callbackF(Xi):

    global Nfeval

    print('pass callback',str(Nfeval))

    print(Nfeval, Xi[0], Xi[1], f(Xi))

    Nfeval += 1

initial_guess = [0, 0]

b = (0.0, 1.0)

b0 = b1 = b

bnb = [b0, b1]

res = minimize(f, initial_guess, bounds=bnb, method='bfgs', callback=callbackF, options={'disp':True})

print (res)

我试图捕获目标函数的最佳结果，但它总是显示 [1, 1]。理想情况下，我应该将两个参数限制在 0 和 1 之间，以最大化 -LL。我做错了什么吗？我想知道是否应该在每次迭代后更新目标函数，但我很困惑如何使其发挥作用。我检查了几个帖子但仍然不确定。其他阅读材料也非常受欢迎。多谢！

pass callback 25

25 0.6870283538140954 0.7403323855238932 143.98656641020855

pass callback 26

26 0.7935216169001177 0.7090801503785442 143.93658208323882

pass callback 27

27 0.8314173041320377 0.7666686643426496 143.84748818067345

pass callback 28

28 0.9264732632840973 0.8980814706430704 143.7237871814941

pass callback 29

29 0.9885339111975429 0.9836968132795704 143.69759782341296

pass callback 30

30 0.999243206123829 0.9988036732413753 143.69694856450647

pass callback 31

31 1.0000109917713558 0.9999811482899945 143.6969451785149

pass callback 32

32 1.0000049364520325 0.99999836986115 143.6969451768374

pass callback 33

33 1.000000303283094 1.000000360615374 143.6969451767528

Optimization terminated successfully.

         Current function value: 143.696945

         Iterations: 9

         Function evaluations: 44

         Gradient evaluations: 11

      fun: 143.6969451767528

 hess_inv: array([[0.2255719 , 0.08676943],

       [0.08676943, 0.21320636]])

      jac: array([1.90734863e-06, 3.81469727e-06])

  message: 'Optimization terminated successfully.'

     nfev: 44

      nit: 9

     njev: 11

   status: 0

  success: True

        x: array([1.0000003 , 1.00000036])

Answer 1

看起来优化器正在 [1,1] 处找到正确的最小值。这是您的函数图：这是我用来生成该图的代码。from scipy.optimize import minimizeimport numpy as npimport matplotlib.pyplot as pltfrom matplotlib import cmdef f(params):    pi12, pi21 = params    LL = 10*np.log(40*60/110**2) + 30*np.log(40*50/110**2) + 20*np.log(20/110*(50/110 + 60/110*pi12)) + \         50*np.log(50/110*(60/110 + 50/110*pi21)) - 110*np.log(40*60/110**2 + 40*50/110**2 + \         20/110*(50/110 + 60/110*pi12) + 50/110*(60/110 + 50/110*pi21))    return -LLdef g(X,Y):    return f([X,Y])initial_guess = [0, 0]b = (0.0, 1.0)b0 = b1 = bbnb = [b0, b1]res = minimize(f, initial_guess, bounds=bnb, method='bfgs')print (res)X = np.arange(0, 1, 0.05)Y = np.arange(0, 1, 0.05)X, Y = np.meshgrid(X, Y)Z = g(X,Y)fig = plt.figure()ax = fig.gca(projection='3d')# Plot the surface.surf = ax.plot_surface(X, Y, Z, cmap=cm.coolwarm,                       linewidth=0, antialiased=False)plt.show()