Scipy.optimize約束最小化誤差

Question

我試圖在其他兩個三個變量函數等於零的約束下最大化三個變量函數func（x，y，z）。

我一直在關注http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html中的“約束最小化標量函數（最小化）”示例。 我將目標函數更改為自己的函數，並將程序調整為（我認為）可以運行三個變量而不是示例中的兩個變量。 這是我的代碼：

import numpy as np
from scipy.optimize import minimize

def zeroth(x):      # The form of the zeroth order contribution
    return x/(1+x**2)

def first(x):       # The form of the first order contribution
    return x/(1+x**2)**2 

def second(x):      # The second order contribution
    return x*(3-x**2)/(1+x**2)**3

def derivZeroth(x):
    return (1-x**2)/(1+x**2)**2

def derivFirst(x):
    return (1-3*x**2)/(1+x**2)**3

def derivSecond(x):
    return 3*(x**4 - 6*x**2 + 1)/(1+x**2)**4

def func(x, sign=1.0):
    """ Objective function """
    return  zeroth(x[0]) + zeroth(x[1]) - zeroth(x[2]) 

def func_deriv(x, sign=1.0):
    """ Derivative of objective function """
    dfdx0 = derivZeroth(x[0])
    dfdx1 = derivZeroth(x[1])
    dfdx2 = -derivZeroth(x[2])
    return np.array([ dfdx0, dfdx1, dfdx2 ])

cons = ({'type': 'eq',
         'fun' : lambda x: np.array([ first(x[0]) + first(x[1]) - first(x[2]) ]),
         'jac' : lambda x: np.array([ derivFirst(x[0]) + derivFirst(x[1]) - derivFirst(x[2])  ])},
        {'type': 'eq',
         'fun' : lambda x: np.array([ second(x[0]) + second(x[1]) - second(x[2]) ]),
         'jac' : lambda x: np.array([ derivSecond(x[0]) + derivSecond(x[1]) -  derivSecond(x[2]) ])})


x0 = [1.0,1.0,1.0]

res = minimize(func, x0, args=(-1.0,), jac=func_deriv,
           constraints=cons, method='SLSQP', options={'disp': True})





print(res.x)

我得到錯誤

ValueError: all the input array dimensions except for the concatenation axis must match exactly

完整的錯誤如下所示：

Traceback (most recent call last):
  File "mycode.py", line 46, in <module>
    constraints=cons, method='SLSQP', options={'disp': True})
  File ".../python2.7/site-packages/scipy/optimize/_minimize.py", line 388, in minimize
    constraints, **options)
  File ".../python2.7/site-packages/scipy/optimize/slsqp.py", line 393, in _minimize_slsqp
    a = vstack((a_eq, a_ieq))
  File ".../python2.7/site-packages/numpy/core/shape_base.py", line 228, in vstack
    return _nx.concatenate([atleast_2d(_m) for _m in tup], 0)
ValueError: all the input array dimensions except for the concatenation axis must match exactly

這是怎么回事？

Answer 1

我認為約束的雅各派成員應具有3的長度。