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Abadie-Type Constraint Qualification for Mathematical Programs with Equilibrium Constraints

  • M.L. Flegel
  • C. Kanzow
Article

Abstract

Mathematical programs with equilibrium constraints (MPEC) are nonlinear programs which do not satisfy any of the common constraint qualifications (CQ). In order to obtain first-order optimality conditions, constraint qualifications tailored to the MPECs have been developed and researched in the past. In this paper, we introduce a new Abadie-type constraint qualification for MPECs. We investigate sufficient conditions for this new CQ, discuss its relationship to several existing MPEC constraint qualifications, and introduce a new Slater-type constraint qualifications. Finally, we prove a new stationarity concept to be a necessary optimality condition under our new Abadie-type CQ.

Keywords

Mathematical programs with equilibrium constraints Abadie constraint qualification Slater constraint qualification optimality conditions 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • M.L. Flegel
    • 1
  • C. Kanzow
    • 2
  1. 1.Institute of Applied Mathematics and StatisticsUniversity of WürzburgAm Hubland, Würzburg Germany
  2. 2.Institute of Applied Mathematics and StatisticsUniversity of WürzburgAm Hubland, Würzburg Germany

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