Abadie-type constraint qualification for mathematical programs with equilibrium constraints. (English) Zbl 1090.90200
Summary: 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.
MSC:
| 90C46 | Optimality conditions and duality in mathematical programming |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
Keywords:
Mathematical programs with equilibrium constraints; Abadie constraint qualification; Slater constraint qualification; optimality conditionsReferences:
| [5] | Flegel, M. L., and Kanzow, C., On the Guignard Constraint Qualification for Mathematical Programs with Equilibrium Constraints, Preprint 248, Institute of Applied Mathematics and Statistics, University of Würzburg, 2002. · Zbl 1147.90397 |
| [11] | Mangasarian, O. L., Nonlinear Programming, SIAM, Philadelphia, Pennsylvania, 1994. |
| [14] | Flegel, M. L., and Kanzow, C., An Abadie- Type Constraint Qualification for Mathematical Programs with Equilibrium Constraints, Preprint, Institute of Applied Mathematics and Statistics, University of Würzburg, 2002. · Zbl 1090.90200 |
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