
Journal of Convex Analysis 19 (2012), No. 4, 9991008 Copyright Heldermann Verlag 2012 SemiInfinite Programming: Strong Stability implies EMFCQ Dominik Dorsch RWTH Aachen, University of Technology, Dept. of Mathematics C, Templergraben 55, 52056 Aachen, Germany dorsch@mathc.rwthaachen.de Harald Günzel RWTH Aachen, University of Technology, Dept. of Mathematics C, Templergraben 55, 52056 Aachen, Germany guenzel@mathc.rwthaachen.de Francisco GuerraVázquez Universidad de las Américas, Escuela de Ciencias, San Andrés Cholula, Puebla 72820, Mexico francisco.guerra@udlap.mx JanJ. Rückmann The University of Birmingham, School of Mathematics, Birmingham B152TT, England J.Ruckmann@bham.ac.uk We consider strongly stable stationary points of semiinfinite 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 MangasarianFromovitz 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: Semiinfinite programming, strongly stable stationary point, extended MangasarianFromovitz constraint qualification. MSC: 90C34, 90C31 [ Fulltextpdf (130 KB)] for subscribers only. 