indicator variable in MILP

I have an indicator variable in my objective function where

I = 0 if x<0 I = 1 if x>= 0

How to write constraints for this indicator variable I in MILP?

Answer 1

[John D'Errico]

So I is not actually a variable in your problem, although you think of it as such. Perhaps as you have written the problem on paper you have some variable I.

I is a function of one of the variables (x). Is I a linear function of x? No. It does not behave linearly with x. Therefore it is a nonlinear function of x.

So you cannot write constraints on it for a MILP solver.

[Nana]

I variable should be indicated in the objective function since I will use it further.

The full objective function is something like this:

minimize (I_pos * x * a) + (I_neg * x * b)

subjected to: 
I_pos = 1 if x >= 0 and 0 if else
I_neg = 1 if x < 0 and 0 if else