  This work continues an ongoing effort to compare non-smooth optimization
problems in abs-normal form to Mathematical Programs with Complementarity
Constraints (MPCCs). We study general Nonlinear Programs with equality and
inequality constraints in abs-normal form, so-called Abs-Normal NLPs, and their
relation to equivalent MPCC reformulations. We introduce the concepts of
Abadie's and Guignard's kink qualification and prove relations to MPCC-ACQ and
MPCC-GCQ for the counterpart MPCC formulations. Due to non-uniqueness of a
specific slack reformulation suggested in [10], the relations are non-trivial.
It turns out that constraint qualifications of Abadie type are preserved. We
also prove the weaker result that equivalence of Guginard's (and Abadie's)
constraint qualifications for all branch problems hold, while the question of
GCQ preservation remains open. Finally, we introduce M-stationarity and
B-stationarity concepts for abs-normal NLPs and prove first order optimality
conditions corresponding to MPCC counterpart formulations.
