Search code examples
pythonnumpymathematical-optimizationipoptgekko

How to solve Absolute Value abs() objective with Python Gekko?

An optimization problem with a squared objective solves successfully with IPOPT in Python Gekko.

from gekko import GEKKO
import numpy as np
m = GEKKO()
x = m.Var(); y = m.Param(3.2)
m.Obj((x-y)**2)
m.solve()
print(x.value[0],y.value[0])

However, when I switch to an absolute value objective np.abs(x-y) (the numpy version of abs) or m.abs(x-y) (the Gekko version of abs), the IPOPT solver reports a failed solution. An absolute value approximation m.sqrt((x-y)**2) also fails.

Failed Solution

from gekko import GEKKO
import numpy as np
m = GEKKO()
x = m.Var(); y = m.Param(3.2)
m.Obj(m.abs(x-y))
m.solve()
print(x.value[0],y.value[0])

I understand that gradient-based solvers don't like functions without continuous first and second derivatives so I suspect that this is happening with abs() where 0 is a point that does not have continuous derivatives. Is there any alternative to abs() to reliably solve an absolute value with gradient-based solvers in Python Gekko?

Solution

  • You can use m.abs2 instead, It takes into account the issue with the derivative and should solve the issue.