demoPOPSolver.py

#!/usr/bin/python3

"""
Demo, how to use the POP Solver.

by Pavel Trutman, pavel.trutman@fel.cvut.cz
"""

from numpy import *
import polyopt

# objective function
# f(x, y) = (x - 1)^2 + (y - 2)^2
#         = x^2 -2*x + y^2 - 4*y + 5
# global minima at (1, 2)
f = {(0, 0): 5, (1, 0): -2, (2, 0): 1, (0, 1): -4, (0, 2): 1}

# constraint function
# g(x, y) = 9 - x^2 - y^2
g = [{(0, 0): 3**2, (2, 0): -1, (0, 2): -1}]

# degree of the relaxation
d = 2

# initialize the solver
POP = polyopt.POPSolver(f, g, d)

# obtain some feasible point for the SDP problem (within ball with radius 3)
y0 = POP.getFeasiblePointFromRadius(3)
# or select some feasible points of the polynomial optimization problem
y0 = POP.getFeasiblePoint([array([[1],[1]]), array([[2],[2]]), array([[-1], [-1]]), array([[-2], [1]]), array([[1], [2]]), array([[0], [2]])])

# enable outputs
POP.setPrintOutput(True)

#solve the problem
x = POP.solve(y0)
print(x)

print('Rank of the moment matrix: ', POP.momentMatrixRank())