CODEWITHSUNDEEP
pythonscipyconstraintsminimize
Fabio Bertellotti
Fabio Bertellotti

Reputation: 53

Scipy minimize .. 'Inequality constraints incompatible'

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])

Upvotes: 0

Views: 4422

Answers (2)

PiWi
PiWi

Reputation: 169

Much later! I ran in a similar problem and found a solution for the SLSQP algorithm (that scipy.optimize.minimize uses by default) to converge: scale the function to minimize to its output is in the same range as input. The error message of SLSLQ 'Inequality constraints incompatible' is not very helpful to hint at that...

Interestingly however, in the case provided in question, SLSLQP answer nowhere near as good as COBYLA answer:

  • SLSQP: -34487
  • COBYLA: -55800

And SLSQP tho it converges, is dependant on scaling factor.

from scipy.optimize import minimize

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]}
)

scaling_coeffs = [0.1, 1, 10, 100, 1000, 10000]

for scaling_coeff in scaling_coeffs:

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

    res1 = minimize(f, x0, constraints=cons, method='SLSQP')
    res2 = minimize(f, x0, constraints=cons, method='cobyla')

    fx1 = res1.fun * scaling_coeff if res1.success else "failed"
    fx2 = res2.fun * scaling_coeff if res2.success else "failed"

    print(scaling_coeff, fx1, fx2)

    # coeff   SLSQP   COBYLA
    # 0.1     failed -55800.0
    # 1       failed -55800.0
    # 10    -33490.0 -55800.0
    # 100   -33490.0 -55800.0
    # 1000  -34487.0 -55800.0
    # 10000 -6025.96 -55800.0

Note: I know that this answer is worse in that case than accepted answer. However I post it because I ran in the same problem and could solve it this way with good result in my case. I had bounds and COBYLA does not accept them (even if you can pass them as constraints, see Does scipy's minimize function with method "COBYLA" accept bounds?)

Upvotes: 0

vperrollaz
vperrollaz

Reputation: 56

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])

Upvotes: 2

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