  We investigate the local topological structure, stationary point sets in
parametric optimization genericly may have. Our main result states that, up to
stratified isomorphism, any such structure is already present in the small
subclass of parametric problems with convex quadratic objective function and
affine-linear constraints.
  In other words, the convex quadratic problems produce a normal form for the
local topological structure of stationary point sets.
  As a consequence we see, as far as no equality constraints are involved, that
the closure of the stationary point set constitutes a manifold with boundary.
The boundary is exactly the violation set of the Mangasarian Fromovitz
constraint qualification.
  A side result states that stationary point sets and violation sets of
Mangasarian Fromovitz constraint qualification carry the same set of possible
local structures as stratified spaces.
