python - How do I use a minimization function in scipy with constraints

Question

I need some help regarding optimisation functions in python(scipy) the problem is optimizing f(x) where x=[a,b,c...n]. the constraints are that values of a,b etc should be between 0 and 1, and sum(x)==1. The scipy.optimise.minimize function seems best as it requires no differential. How do I pass the arguments?

Creating an ndarray using permutation is too long. My present code as below:-

import itertools as iter
all=iter.permutations([0.0,.1,.2,.3,.4,.5,.6,.7,.8,.9,1.0],6) if sum==1
all_legal=[]
for i in all:
if np.sum(i)==1:
    #print np.sum(i)
    all_legal.append(i)
print len(all_legal)
lmax=0
sharpeMax=0
for i in all_legal:
    if sharpeMax<getSharpe(i):
        sharpeMax=getSharpe(i)
        lmax=i

Answer 1

You can do a constrained optimization with COBYLA or SLSQP as it says in the docs.

from scipy.optimize import minimize

start_pos = np.ones(6)*(1/6.) #or whatever

#Says one minus the sum of all variables must be zero
cons = ({'type': 'eq', 'fun': lambda x:  1 - sum(x)})

#Required to have non negative values
bnds = tuple((0,1) for x in start_pos)

Combine these into the minimization function.

res = minimize(getSharpe, start_pos, method='SLSQP', bounds=bnds ,constraints=cons)