  Given a non-convex optimization problem, we study conditions under which
every Karush-Kuhn-Tucker (KKT) point is a global optimizer. This property is
known as KT-invexity and allows to identify the subset of problems where an
interior point method always converges to a global optimizer. In this work, we
provide necessary conditions for KT-invexity in n-dimensions and show that
these conditions become sufficient in the two-dimensional case. As an
application of our results, we study the Optimal Power Flow problem, showing
that under mild assumptions on the variable's bounds, our new necessary and
sufficient conditions are met for problems with two degrees of freedom.
