I am trying to maximize a three variable function, func(x,y,z), under the constraint that two other three variable functions are equal to zero.
I was following the "Constrained minimization of multivariate scalar functions (minimize)" example from http://docs.scipy.org/doc/scipy/reference/tutorial/optimize.html . I changed the objective function to my own and adjusted the program to (I thought) run for three variables instead of the example's two. Here's my code:
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)
I get the error
ValueError: all the input array dimensions except for the concatenation axis must match exactly
The full error looks like this:
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
What's going on?
我认为约束的雅各派成员应具有3的长度。
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