Minimize System of Equations with constraints (scipy.optimize.minimize)

问题

The following code:

import numpy as np
from scipy.optimize import minimize

def eq( p ):
    s1,s2,s3 = p 
    f1 = 1.1**3 / s1*1.1**1+s2*1.1**2+s3*1.1**3
    f2 = 0.9**1 / s1*0.9**1+s2*0.9**2+s3*0.9**3
    return (f1, f2) 

bnds = ( (0, None), (0, None), (0, None) )
cons = ( { 'type' : 'ineq', 'fun': lambda p: p[0]+[p1]+[p2] - 1} )


minimize( eq, (0.3,0.3,0.3),  bounds=bnds, constraints=cons )

throws the error

TypeError: unsupported operand type(s) for -: 'tuple' and 'tuple'

I want to minimize f1 and f2 such that the s_t > 0 and sum s_t <= 1, for t = 1, 2, 3.

回答1:

minimize( eq, (0.3,0.3,0.3),  bounds=bnds, constraints=cons )

The second argument should be an ndarray not a tuple. The args tuple comes after the initial guess (x0).

http://docs.scipy.org/doc/scipy-0.17.0/reference/generated/scipy.optimize.minimize.html

回答2:

The second parameter should be of type ndarray, try using

 minimize( eq, np.ndarray([0.3,0.3,0.3]),  bounds=bnds, constraints=cons )

来源：https://stackoverflow.com/questions/36108921/minimize-system-of-equations-with-constraints-scipy-optimize-minimize