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# The analytic centering with cone constraints example of section 9.1
# (Problems with nonlinear objectives).
from cvxopt import matrix, log, div, spdiag
from cvxopt import solvers
def F(x = None, z = None):
if x is None: return 0, matrix(0.0, (3,1))
if max(abs(x)) >= 1.0: return None
u = 1 - x**2
val = -sum(log(u))
Df = div(2*x, u).T
if z is None: return val, Df
H = spdiag(2 * z[0] * div(1 + u**2, u**2))
return val, Df, H
G = matrix([
[0., -1., 0., 0., -21., -11., 0., -11., 10., 8., 0., 8., 5.],
[0., 0., -1., 0., 0., 10., 16., 10., -10., -10., 16., -10., 3.],
[0., 0., 0., -1., -5., 2., -17., 2., -6., 8., -17., -7., 6.]
])
h = matrix(
[1.0, 0.0, 0.0, 0.0, 20., 10., 40., 10., 80., 10., 40., 10., 15.])
dims = {'l': 0, 'q': [4], 's': [3]}
sol = solvers.cp(F, G, h, dims)
print("\nx = \n")
print(sol['x'])
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