convert complementary slackness to mixed integer linear constraints in YALMIP

[P11GH]

I am trying to solve a linear programming with kkt conditions, i.e., primal constraints, dual constraints, and complementary slackness. I want to convert complementary slackness to mixed integer linear constraints with the big-M method and then solve the kkt conditions with solvers for mixed integer linear programming.
I tried:

1. the kkt command in YALMIP. But I cannot find a way to convert the complementary slackness to mixed linear constraints
2. the dualize command in YALMIP. But I cannot find a way to create dual variables automatically and thus cannot encode the mixed linear constraints for the complementary slackness.
   Does anyone know any way to get the complementary slackness and convert it to the mixed integer linear constraints in YALMIP?

ps: As there are a lot of primal variables and primal constraints, manully formulating everything is time-consuming and easy to get bugs. I tried this way, but failed.

[johanlofberg]

the kkt operator uses https://yalmip.github.io/command/complements/

[P11GH]

Yes, thank you very much for reminding me.
Duality of mixied integer problems is very complex. So I am actually trying to get a feasible solution that is not bad in optimality with kkt. Can I get such a solution with the kkt operator?

[johanlofberg]

My guess is that you can construct MILP problems where faux-kkt would generate arbitrary garbage.

[P11GH]

perhaps, KKT conditions for mixed integer problems does not guarantee any optimality.

[johanlofberg]

Absolutely not. I took it for granted that you already knew that kkt conditions are invalid for problems with binary variables.

[P11GH]

yes, I knew that. Thank you for the help.