In the below, we try to minimize an objective which does nothing but sum all 100 of its arguments, under the constraint that each argument is no less than -20. The optimal solution is clearly using -20 for each argument.

If I pass the constraint as 100 separate constraints, fmin_cobyla behaves as expected, but if I combine them all into a single one saying lambda x: x.min() + 20 (if the smallest element of x is greater than -20, then all of them are), then the result violates the constraint.

As far as I can tell, there is nothing in the docs requiring the constraints to take a particular form, e.g. be linear; in particular the example provided contains a quadratic constraint.

Reproducing code example:

def con(x): return x.min() + 20
print(scipy.optimize.fmin_cobyla(np.sum, np.zeros(100, dtype=np.float), cons=[con]))
# Prints [-25.62157867 -27.18539934 -27.38919247 ...

cons = [lambda x, m=n: x[m] + 20 for n in range(100)]
print(scipy.optimize.fmin_cobyla(np.sum, np.zeros(100, dtype=np.float), cons=cons))
# Prints [-20.         -20.         -20. ...

It also works fine if I instead let con return an array (although it's not super clear from the documentation that that's possible):

def con(x): return x + 20
print(scipy.optimize.fmin_cobyla(np.sum, np.zeros(100, dtype=np.float), cons=[con]))
# Prints [-20.         -20.         -20. ...

Scipy/Numpy/Python version information:

1.6.1 1.19.2 sys.version_info(major=3, minor=7, micro=6, releaselevel='final', serial=0)