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On stability and stationary points in nonlinear optimization

Published online by Cambridge University Press:  17 February 2009

J. Guddat ,
H. Th. Jongen  and
J. Rueckmann
J. Guddat
Affiliation:
Humboldt-University, Berlin, German Democratic Republic
H. Th. Jongen
Affiliation:
Twente University of Technology, Enschede, The Netherlands
J. Rueckmann
Affiliation:
Technical University Leipzig, Leipzig, German Democratic Republic
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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 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).

Type
Research Article
Information
The ANZIAM Journal , Volume 28 , Issue 1 , July 1986 , pp. 36 - 56
Copyright
Copyright © Australian Mathematical Society 1986

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