  This paper pursues a two-fold goal. Firstly, we aim to derive novel
second-order characterizations of important robust stability properties of
perturbed Karush-Kuhn-Tucker systems for a broadclass of constrained
optimization problems generated by parabolically regular sets. Secondly, the
obtained characterizations are applied to establish well-posedness and
superlinear convergence of the basic sequential quadratic programming method to
solve parabolically regular constrained optimization problems.
