scipy.optimize.minimize 抛出错误：只有 size-1 数组可以转换为 Python 标量

Question

我想最小化具有某些约束的函数。在下面的代码中，A= 4 x 4 矩阵，v= 4 x 1 向量，alpha 是随机标量值。为了避免错误“只有 size-1 数组可以转换为 Python 标量”，我对约束和目标函数进行了向量化。然而，仍然没有运气，并且出现了同样的错误。

import random
from scipy.optimize import minimize
from numpy.linalg import norm

def calculateV(params):
    return norm(params)

#Declaring the equation here
def objective(x):
    alpha = x[0]
    v=x[1:len(x)]
    vnorm=calculateV(v)
    return alpha+(vnorm/2)

#Need to vectorize the objective function to avoid only size 1 arrays can be converted 
#to Python scalars
f=np.vectorize(objective)

#Declaring the constraint here
def constraint(x):
   alpha=x[0]
   v=x[1:len(x)]
   vnorm=calculateV(v)
   return A*v-alpha
c=np.vectorize(constraint)   

#starting values
startalpha=random.random();
shape=(4,1)
startv=np.random.uniform(0,1,shape)
val_start=[startalpha,startv] 

cons={'type':'ineq','fun':c}

result=minimize(f,val_start,constraints=cons,options={"disp":True})   

if result.success:
  print("Success")
else:
  print("Sorry could not compute a minimum") 

回溯错误消息是：-

------Start--------
TypeError: only size-1 arrays can be converted to Python scalars

The above exception was the direct cause of the following exception:

Traceback (most recent call last):
  File "<ipython-input-4-a3839c47e06a>", line 46, in <module>
    result=minimize(objective,val_start,constraints=cons,options={"disp":True})
  File "/usr/local/lib/python3.7/dist-packages/scipy/optimize/_minimize.py", line 618, in minimize
    constraints, callback=callback, **options)
  File "/usr/local/lib/python3.7/dist-packages/scipy/optimize/slsqp.py", line 308, in _minimize_slsqp
    x = asfarray(x0).flatten()
  File "<__array_function__ internals>", line 6, in asfarray
  File "/usr/local/lib/python3.7/dist-packages/numpy/lib/type_check.py", line 114, in asfarray
    return asarray(a, dtype=dtype)
ValueError: setting an array element with a sequence.

------End--------
/usr/local/lib/python3.7/dist-packages/scipy/optimize/_minimize.py:479: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.
  x0 = np.asarray(x0)

Answer 1

我猜没有没有正确的错误消息，但是这里有一些看起来可疑的代码。

In [236]: startalpha=random.random();
     ...: shape=(4,1)
     ...: startv=np.random.uniform(0,1,shape)
     ...: val_start=[startalpha,startv]
     ...: 
In [237]: val_start
Out[237]: 
[0.272350113689266,
 array([[0.12736234],
        [0.69036025],
        [0.24118139],
        [0.68033726]])]

查看最小化文档，并告诉我这是否是合法参数。