indicator variable in MILP

2016 5 8
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更新时间：2016 5 8
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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?

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John D'Errico
John D'Errico 2016-5-8
编辑：John D'Errico 2016-5-8

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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.

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Nana
Nana 2016-5-8
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

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2016-5-8

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