Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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, México

francisco.guerra@udlap.mx

Jan-J. Rückmann

The University of Birmingham, School of Mathematics, Birmingham B152TT, England

J.Ruckmann@bham.ac.uk

Keywords

  • Semi-infinite programming
  • strongly stable stationary point
  • extended Mangasarian-Fromovitz constraint qualification

Mathematics Subject Classification

90C34, 90C31

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Suggested citation

D. Dorsch, H. Günzel, F. Guerra-Vázquez, J.-J. Rückmann. “Semi-Infinite Programming: Strong Stability implies EMFCQ.” Journal of Convex Analysis 19 (2012), No. 4, 999–1008. https://doi.org/10.68381/jca19052

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Published by Heldermann Verlag, 2012. Rights now held by Banach Press LLC.