##
**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 conditions
PDF
BibTeX
XML
Cite

\textit{M. L. Flegel} and \textit{C. Kanzow}, J. Optim. Theory Appl. 124, No. 3, 595--614 (2005; Zbl 1090.90200)

Full Text:
DOI

### References:

[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 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.