Does scipy's minimize function with method "COBYLA" accept bounds?

Question

I'm using the algorithm 'COBYLA' in scipy's optimize.minimize function (v.0.11 build for cygwin). I observed that the parameter bounds seems not to be used in this case. For instance, the simple example:

from scipy.optimize import minimize

def f(x):
    return -sum(x)

minimize(f, x0=1, method='COBYLA', bounds=(-2,2))

returns:

status: 2.0
nfev: 1000
maxcv: 0.0
success: False
fun: -1000.0
x: array(1000.0)
message: 'Maximum number of function evaluations has been exceeded.'

instead of the expected 2 for x.

Did anyone perceived the same problem? Is there a known bug or documentation error? In the scipy 0.11 documentation, this option is not excluded for the COBYLA algorithm. In fact the function fmin_cobyla doesn't have the bounds parameter. Thanks for any hint.

Answer 1

You can formulate the bounds in the form of constraints

import scipy
#function to minimize
def f(x):
    return -sum(x)
#initial values
initial_point=[1.,1.,1.]    
#lower and upper bound for variables
bounds=[ [-2,2],[-1,1],[-3,3]   ]

#construct the bounds in the form of constraints
cons = []
for factor in range(len(bounds)):
    lower, upper = bounds[factor]
    l = {'type': 'ineq',
         'fun': lambda x, lb=lower, i=factor: x[i] - lb}
    u = {'type': 'ineq',
         'fun': lambda x, ub=upper, i=factor: ub - x[i]}
    cons.append(l)
    cons.append(u)

#similarly aditional constrains can be added

#run optimization
res = scipy.optimize.minimize(f,initial_point,constraints=cons,method='COBYLA')
#print result
print res

Note that the minimize function will give the design variables to the function. In this case 3 input variables are given with 3 upper and lower bounds. the result yields:

   fun: -6.0
   maxcv: -0.0
 message: 'Optimization terminated successfully.'
    nfev: 21
  status: 1
 success: True
       x: array([ 2.,  1.,  3.])