Stationary Point Set: Topological Universality of Convex Quadratic Problems

Harald G├╝nzel

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
are already present in convex quadratic optimization.

We can use natural embeddings between stationary point sets and violation sets
of the Mangasarian-Fromovitz constraint qualification (of different problem size)
to make the universality theorem prove some other topological properties.