Journal of Convex Analysis 19 (2012), No. 4, 999--1008
Copyright Heldermann Verlag 2012
Semi-Infinite Programming: Strong Stability implies EMFCQ
Dominik Dorsch
RWTH Aachen, University of Technology, Dept. of Mathematics C, Templergraben 55, 52056 Aachen, Germany
dorsch@mathc.rwth-aachen.de
Harald Günzel
RWTH Aachen, University of Technology, Dept. of Mathematics C, Templergraben 55, 52056 Aachen, Germany
guenzel@mathc.rwth-aachen.de
Francisco Guerra-Vázquez
Universidad de las Américas, Escuela de Ciencias, San Andrés Cholula, Puebla 72820, Mexico
francisco.guerra@udlap.mx
Jan-J. Rückmann
The University of Birmingham, School of Mathematics, Birmingham B152TT, England
J.Ruckmann@bham.ac.uk
We consider strongly stable stationary points of semi-infinite programming problems. The concept of strong stability was introduced by Kojima for finite programming problems and it refers to the local existence and uniqueness of a stationary point for each sufficiently small perturbed problem where perturbations up to second order are allowed. Under the extended Mangasarian-Fromovitz constraint qualification (EMFCQ) strong stability can be characterized algebraically by the first and second derivatives of the describing functions. In this paper we show that strong stability implies that EMFCQ holds at the stationary point under consideration.
Keywords: Semi-infinite programming, strongly stable stationary point, extended Mangasarian-Fromovitz constraint qualification.
MSC: 90C34, 90C31
[ Fulltext-pdf (130 KB)] for subscribers only.