about bilevel probelm and KKT condition

[覃岭]

Hi johan

I realize that we can use either kkt method or solvebilevel function to handle the bilevel problems.

1. but I know that kkt condition is nonlinear, if my solver is cplex, can I directly solve it?

2. if the bilevel problem has a MILP inner problem with some integer variables,  are above methods still valid?( only valid for Linear inner problem? )

[Johan Löfberg]

cplex cannot be used directly. However, for QP bilevel programs, you can reformulate it to a problem which can be solved using cplex

http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Examples.BilevelProgramming
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Commands.Kkt
http://users.isy.liu.se/johanl/yalmip/pmwiki.php?n=Tutorials.BilevelProgramming

Integer variables in the inner problem is extremely hard. No simple way to do it, you would have to look at current research literature on algorithms to attack this.

[覃岭]

I see, thanks.