Semidefinite o-pi-timality

Happy $\pi$ Day! If other methods fail, you can always compute $\pi$ with the MOSEK semidefinite optimizer. We leave the details as an interesting exercise for the curious readers. Some hints are hidden in our Modeling Cookbook .

	from mosek.fusion import *
	import mosek.fusion.pythonic
	import numpy as np
	def showmepi(d, m):
	A = np.eye(m, k = 1) - np.eye(m)
	with Model() as M:
	S = M.variable(Domain.inPSDCone(m))
	M.constraint(Expr.dot(S, np.eye(m)) == 1)
	M.objective(ObjectiveSense.Maximize, Expr.dot(S, A + A.T))
	M.solve()
	print(f'{np.sqrt(-M.primalObjValue())*(m+1):.{d}f}')
	for d, m in enumerate([5, 20, 200, 400, 600, 1600]):
	showmepi(d + 1, m)
	'''
	output:
	3.1
	3.14
	3.142
	3.1416
	3.14159
	3.141592
	'''

view raw showmepi.py hosted with ❤ by GitHub