I guess setting maxeval or maxtime must guarantee that optimization algorithms finish anyway (or possibly raise an exception). With the following settings, opt.optimize() never returns (though I can make a workaround, for example, by changing the algorithm or putting other stopping criteria).

import nlopt
import numpy as np

def f(x, _grad):
    return (2 - np.cos(x[0]) + x[1] ** 2) ** 2

opt = nlopt.opt(nlopt.LN_COBYLA, 2)
opt.set_min_objective(f)
opt.set_maxeval(668)  # doesn't seems to work
opt.set_maxtime(1.0)  # doesn't seems to work
opt.optimize([0, 0])  # never returns

If I use opt.set_maxeval(667) in the above code, then somehow it returns with the correct answer [0, 0].

Just in case, I am testing with the following versions (on Google Colab):

Python: 3.6.9
nlopt: 2.6.1

(I'm not sure why pip doesn't pick up 2.6.2).