Scipy minimize .. 'Inequality constraints incompatible'

Question

hi im trying to minimize a simple 3 variable function with some range costraints in the x variables .. but im getting 'Inequality constraints incompatible - any idea ? thanks !!

from scipy.optimize import minimize

def f(x):
    return (int(558*x[0]*x[1]*x[2])-(x[2]*(558-int(558*x[0])))-(x[2]*558))

x0 = [0.4, 1.0, 2.0]

#real data Ranges 
#x[0] 0..1    
#x[1] 1..3
#x[2] 5..50

cons=( 
        {'type': 'ineq','fun': lambda x: x[0]},
        {'type': 'ineq','fun': lambda x: 1-x[0]},
        {'type': 'ineq','fun': lambda x: x[1]-1},
        {'type': 'ineq','fun': lambda x: 3-x[1]},
        {'type': 'ineq','fun': lambda x: x[2]-5},
        {'type': 'ineq','fun': lambda x: 50-x[2]}
)

res = minimize(f, x0, constraints=cons)
print(res)

full result is

    fun: -33490.99993615066
     jac: array([ 6.7108864e+07,  6.7108864e+07, -8.9300000e+02])
 message: 'Inequality constraints incompatible'
    nfev: 8
     nit: 2
    njev: 2
  status: 4
 success: False
       x: array([ 0.4       ,  1.        , 49.99999993])

Answer 1

Hello I suspect that the problem comes from the numerical method used.

By default with constraints, minimize use Sequential Least Squares Programming (SLSQP) which is a gradient method. Therefore the function to be minimized has to be regular, but given your use of int it is not.

Using the alternative method: Constrained Optimization BY Linear Approximation (COBYLA) which is of a different nature I get the following

from scipy.optimize import minimize

def f(x):
    return (int(558*x[0]*x[1]*x[2])-(x[2]*(558-int(558*x[0])))-(x[2]*558))

x0 = [0.4, 1.0, 2.0]

#real data Ranges 
#x[0] 0..1    
#x[1] 1..3
#x[2] 5..50

cons=( 
        {'type': 'ineq','fun': lambda x: x[0]},
        {'type': 'ineq','fun': lambda x: 1-x[0]},
        {'type': 'ineq','fun': lambda x: x[1]-1},
        {'type': 'ineq','fun': lambda x: 3-x[1]},
        {'type': 'ineq','fun': lambda x: x[2]-5},
        {'type': 'ineq','fun': lambda x: 50-x[2]}
)

res = minimize(f, x0, constraints=cons, method="cobyla")
print(res)

with the display

     fun: -55800.0
   maxcv: 7.395570986446986e-32
 message: 'Optimization terminated successfully.'
    nfev: 82
  status: 1
 success: True
       x: array([-7.39557099e-32,  1.93750000e+00,  5.00000000e+01])