Bi-level Integer Programming

[Sagnik BasuMallik]

Can someone give me an example or point to resources on how to write bi-level MILP in Gurobi?

[Tobias Achterberg]

This is not that easy. Just to be sure, we are talking about a bilevel problem in which
the optimality to some subproblem on a subset of the variables is a constraint of the
master problem.

In some cases you can model the master problem as a MILP and add a lazy constraint
callback to enforce the optimality criterion of the subproblem. But this depends on the
structure of the subproblem.

Regards,

Tobias

[Sagnik BasuMallik]

Thank you Tobias for explaining. Let's say we have the following simple example:

How can we re-write this in Gurobi? Thank you again for your help

[Sagnik BasuMallik]

Or we can use this very popular example ... How can we re-write this in Gurobi?

[Tobias Achterberg]

With quadratic objective functions it gets even more complicated. I don't know, I am not
an expert in bilevel programming. You should read some papers about this or ask somewhere
else. Sorry.

Regards,

Tobias