# Do the KKT conditions hold for mixed integer nonlinear problems?

I was wondering if the KKT conditions are applicable for for MINLPs, and if not, why not? What about the case when the integer variables are modeled using constraints involving just continuous variables?

• Would you see this link? Oct 13 '19 at 6:16

It's certainly possible to enforce integrality constraints using continuous variables. For example, the constraint that $$x_{i}$$ is 0 or 1 can be written as the nonconvex nonlinear equality constraint $$x_{i}(1-x_{i})=0$$. You could apply the KKT conditions to such a problem, but you would end up with locally optimal points for every possible combination of the integer variable values.