Scipy optimize.minimize exits successfully when constraints aren't satisfied

Question

I've been using scipy.optimize.minimize (docs)

and noticed some strange behavior when I define a problem with impossible to satisfy constraints. Here's an example:

from scipy import optimize

# minimize f(x) = x^2 - 4x
def f(x):
    return x**2 - 4*x

def x_constraint(x, sign, value):
    return sign*(x - value)

# subject to x >= 5 and x<=0 (not possible)
constraints = []
constraints.append({'type': 'ineq', 'fun': x_constraint, 'args': [1, 5]})
constraints.append({'type': 'ineq', 'fun': x_constraint, 'args': [-1, 0]})

optimize.minimize(f, x0=3, constraints=constraints)

Resulting output:

fun: -3.0
     jac: array([ 2.])
 message: 'Optimization terminated successfully.'
    nfev: 3
     nit: 5
    njev: 1
  status: 0
 success: True
       x: array([ 3.])

There is no solution to this problem that satisfies the constraints, however, minimize() returns successfully using the initial condition as the optimal solution.

Is this behavior intended? If so, is there a way to force failure if the optimal solution doesn't satisfy the constraints?

Answer 1

This appears to be a bug. I added a comment with a variation of your example to the issue on github.

If you use a different method, such as COBYLA, the function correctly fails to find a solution:

In [10]: optimize.minimize(f, x0=3, constraints=constraints, method='COBYLA')
Out[10]: 
     fun: -3.75
   maxcv: 2.5
 message: 'Did not converge to a solution satisfying the constraints. See `maxcv` for magnitude of violation.'
    nfev: 7
  status: 4
 success: False
       x: array(2.5)