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.
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Communicated by Z. Q. Luo
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Flegel, M., Kanzow, C. Abadie-Type Constraint Qualification for Mathematical Programs with Equilibrium Constraints. J Optim Theory Appl 124, 595–614 (2005). https://doi.org/10.1007/s10957-004-1176-x
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DOI: https://doi.org/10.1007/s10957-004-1176-x