Stationary Point Set: Topological Universality of Convex Quadratic Problems

Harald Günzel

We observe that the jet-space which is
used to describe stationary points,
Fritz-John-points and some basic constraint qualifications,
is diffeomorphic to the product of state- and parameter-space
of a natural (parametric) family of convex quadratic problems.

Since the diffeomorphism used to establish the latter property
is just the corresponding jet-extension,
this shows the topological universality of the quadratic family,
i.e. topological properties of stationary point sets
that are generically possible in general parametric optimization problems