The crease structure of the Karush–Kuhn–Tucker set in parametric optimization

We study optimization problems depending on a parameter vector y. In particular, we consider the crease structure of the set Sigma of pairs (x, y) where x is a Karush–Kuhn–Tucker point of the problem associated with parameter y; the Mangasarian–Fromovitz constraint qualification is assumed to hold. We present a lower bound for the fineness of Whitney regular stratifications of Sigma. This provides an approximation of its crease structure.