On stability and stationary points in nonlinear optimization
J. Guddat, Hubertus Th. Jongen, Jan Rueckmann · ANZIAM Journal · 1986
This paper presents three theorems concerning stability and stationary points of the constrained minimization problem: In summary, we prove that, given the Mangasarian-Fromovitz constraint qualification (MFCQ), the feasible setM[H, G] is a topological manifold with boundary, with specified dimension; (ℬ) a compact feasible setM[H, G] is stable (perturbations ofHandGproduce homeomorphic feasible sets) if and only if MFCQ holds; under a stability condition, two lower level sets offwith a Kuhn-Tucker point between them are homotopically related by attachment of ak-cell (kbeing the stationary index in the sense of Kojima).