I tried minimum variance optimization using two methods and both give different weights even though the formulation is the same? How is that possible? Any optimization experts in the forum please help?
The first method uses cvxopt (I like this more):
def getWeights(covariance, signal):
P = matrix(covariance)
(m, m) = np.shape(covariance)
q = matrix(-signal, (m, 1))
A = matrix([1.] * m, (1, m))
b = matrix(0., (1,1))
res = solvers.qp(P=P, q=q, A=A, b=b)
return res['x'], res['status'] The second method uses scipy minimize cobyla:
def getWeights(cov, signal):
cons = []
(m,m) = np.shape(cov)
cons.append({'type': 'ineq', 'fun': lambda x: np.sum(x)})
cons.append({'type': 'ineq', 'fun': lambda x: -np.sum(x)})
for i in range(0, m):
cons.append({'type': 'ineq', 'fun': lambda x, i=i: 1 - x[i]})
x0 = [1.] * m
res = minimize(lambda x: np.dot(np.dot(x.T, cov), x) + np.dot(x, -signal), x0,
constraints = cons, method='cobyla',options={'maxiter':20000})
print res.message
return res.x, res.status 