Linearization of bilinear terms

Question

I want to linearize the product of two continuous variables for an optimization problem.

I have tried McCormick relaxation and piece-wise McCormick relaxation, but those relaxation are not tight enough for my problem.

Does anyone know any good trick to linearize the bilinear terms? The method that requires the least number of binary variables would be great.

Thank you,

Answer 1

You're out of luck. If both variables are continuous, their product can not be linearized. Face the music, you have a nonlinear model. If relaxations are not good enough for you, you'll need a nonlinear solver.

If one of the variables were binary, you could use big-M modeling. But that doesn't apply in your case.

Answer 2

Have a look on enter link description here. This article introduces 10 methods for your problem.