Abadie-Type Constraint Qualification for Mathematical Programs with Equilibrium Constraints |
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| Authors: | ML Flegel C Kanzow |
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| Institution: | (1) Institute of Applied Mathematics and Statistics, University of Würzburg, Am Hubland, Würzburg, Germany;(2) Institute of Applied Mathematics and Statistics, University of Würzburg, Am Hubland, Würzburg, Germany |
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| 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.Communicated by Z. Q. Luo |
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| Keywords: | Mathematical programs with equilibrium constraints Abadie constraint qualification Slater constraint qualification optimality conditions |
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