Solving problems with no constraints

[andreadelprete]

Hi,

first of all, thanks for this package, it is really what I was looking for! I'm trying to use it to optimize a simple 1d polynomial, with no constraints, but I'm getting this error:

Traceback (most recent call last):
  File "/home/student/repos/polyopt/demoPOPSolver.py", line 27, in <module>
    POP = polyopt.POPSolver(f, g, d)
  File "/home/student/repos/polyopt/polyopt/POPSolver.py", line 37, in __init__
    if max(gDegsHalf) > d:
ValueError: max() arg is an empty sequence

I guess the solver is not done for the unconstrained case. I was able to get around this by adding a dummy constraint (x+100>=0). Here is the code I'm running now:

f = {(0,): 5, (1,): -2, (2,): 1}
g = [{(0,): 1e2, (1,): 1,}] # constraint function x + 1e2 >=0
d = 2
POP = polyopt.POPSolver(f, g, d)
y0 = POP.getFeasiblePoint([array([[1]]), array([[2]]), array([[-1]]), array([[-2]])])
POP.setPrintOutput(False)
x = POP.solve(y0)

However, I still get an error:

    x = POP.solve(y0) #solve the problem
  File "/home/student/repos/polyopt/polyopt/POPSolver.py", line 80, in solve
    y = self.SDP.solve(startPoint, self.SDP.dampedNewton)
  File "/home/student/repos/polyopt/polyopt/SDPSolver.py", line 188, in solve
    x0 = method(start)
  File "/home/student/repos/polyopt/polyopt/SDPSolver.py", line 314, in dampedNewton
    FdLN = Utils.LocalNormA(Fd, Fdd)
  File "/home/student/repos/polyopt/polyopt/utils.py", line 29, in LocalNormA
    return sqrt(dot((solve(hessian, u)).T, u))[0,0]
  File "<__array_function__ internals>", line 6, in solve
  File "/home/student/.local/lib/python3.5/site-packages/numpy/linalg/linalg.py", line 399, in solve
    r = gufunc(a, b, signature=signature, extobj=extobj)
  File "/home/student/.local/lib/python3.5/site-packages/numpy/linalg/linalg.py", line 97, in _raise_linalgerror_singular
    raise LinAlgError("Singular matrix")
numpy.linalg.LinAlgError: Singular matrix

This time I'm not sure what the problem is. Any suggestion? Moreover, would it be simple to modify the code to handle unconstrained minimization?