Different versions of CVXPY generates different results.

Question

Due to the lack of knowledge of CVXPY, I have a problem with reconciling a simple optimization problem's results when using different versions of it.

When I use CVXPY with version 0.4.5 I wrote my problem as:

import numpy as np
from cvxpy import * 

n = 5
np.random.seed(123)
g1 = np.random.rand(2*n, 1)
H1 = np.eye(2*n)
w = Variable(2*n)
gamma = Parameter(sign="positive")
ret = -g1.T*w
risk = quad_form(w, H1)
prob = Problem(Maximize(ret - gamma*risk), 
               [w >= 0])
gamma.value = 0.5
prob.solve()
res = w.value

and the res equals to:

 res = [[  2.86653834e-12],
    [  2.47912037e-11],
    [  3.73027873e-11],
    [  7.13532730e-12],
    [  2.31133274e-12],
    [  1.27710498e-11],
    [ -2.50944234e-12],
    [  3.15803733e-12],
    [  9.90353521e-12],
    [  1.46452182e-11]]

However, When I use CVXPY with version 1.0.8, I type almost the same codes as follows:

n = 5 
np.random.seed(123)
g1 = np.random.rand(2*n, 1)
H1 = np.eye(2*n)
w = Variable(2*n)
gamma = Parameter(nonneg=True)
ret = -g1.T*w
risk = quad_form(w, H1)
prob = Problem(Maximize(ret - gamma*risk), 
               [w >= 0])
gamma.value = 0.5
prob.solve()
res = w.value

The result is:

(Pdb) res
    array([6.66098380e-25, 2.73633363e-25, 2.16955532e-25, 5.27275998e-25,
   6.88070573e-25, 4.04646723e-25, 9.37904145e-25, 6.54954091e-25,
   4.60002892e-25, 3.75018828e-25])

The only difference I made when using version 1.0.8 of CVXPY is that I use attribute 'nonneg=True' instead of 'sign=positive' which I think they are essentially the same thing. Can someone help me out here? What are the possible reasons that the results are so different?

Many thanks

Answer 1

CVXPY 1.0 uses the OSQP solver for problems like yours, whereas CVXPY 0.4 uses ECOS. That's why the results differ. But ultimately numbers very close to zero should be treated as zero. If your program behaves differently if the output is -1e-12 versus 1e-12 you may want to make the program less sensitive.