Hi all, Take the nonlinear inequality: z >= C + Axy where z is continuous, C contains a bunch of linear stuff, A is a real variable, and x and y are binary variables. I've been having headaches over how to linearize this for a few days, or at least to prove it is not possible. Any input is appreciated. asked 30 Nov '13, 19:25 LC Coelho 
First, replace the \(xy\) term with a new variable \( w:=xy\) using this idea. Then you can replace the term \(Aw \), e.g., using this idea, assuming that \(A\) is bounded. answered 30 Nov '13, 20:39 Austin Buchanan This does not work because one assumes that the original constraint is an equality. In my case, it is a >=.
(30 Nov '13, 20:42)
LC Coelho
2
It should work. Let your constraint be z>=C+v where you enforce v=Aw as the second link suggests.
(30 Nov '13, 20:46)
Austin Buchanan
I'll give it another try tomorrow morning and I'll come back here later. Thanks Austin.
(30 Nov '13, 21:43)
LC Coelho
1
@LC Coelho: If you follow your own advice, things should go just fine ;) [...depending on how you define \(z\) – if it's a continuous variable, then an additional \(z \geq 0\) – as in the formulation suggested by @Austin – is required.]
(01 Dec '13, 05:23)
fbahr ♦
Thanks Austin and Fbahr, you were both right. I was trying to rewrite everything at once. By adding several steps and intermediate variables those tips really work.
(01 Dec '13, 22:57)
LC Coelho
