Code:
from mosek.fusion import *
from math import sqrt
def pi(n):
M = Model()
x = M.variable(n, Domain.inQCone())
M.constraint(Expr.mulElm( range(1,n), x.slice(1,n) ),
Domain.greaterThan(sqrt(6)))
M.objective(ObjectiveSense.Minimize, x.index(0))
M.solve()
return M.primalObjValue()
print pi(100)
print pi(1000)
print pi(10000)
print pi(100000)
print pi(200000)
Output:
3.13198074852
3.14063710035
3.14149715507
3.14158310484
3.14158824714
Hint:
$\sum_{i=1}^\infty\frac{1}{i^2}=\frac{\pi^2}{6}$.
