This paper presents three theorems concerning stability and stationary points of the constrained minimization problem:
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS033427000000518X/resource/name/S033427000000518X_eqnU1.gif?pub-status=live)
In summary, we prove
that, given the Mangasarian-Fromovitz constraint qualification (MFCQ), the feasible set M[H, G] is a topological manifold with boundary, with specified dimension; (ℬ) a compact feasible set M[ H, G] is stable (perturbations of H and G produce homeomorphic feasible sets) if and only if MFCQ holds;
under a stability condition, two lower level sets of f with a Kuhn-Tucker point between them are homotopically related by attachment of a k-cell (k being the stationary index in the sense of Kojima).