Constraint qualifications and stationarity concepts for mathematical programs with equilibrium constraints

An exhaustive discussion of constraint qualifications (CQ) and stationarity concepts for mathematical programs with equilibrium constraints (MPEC) is presented. It is demonstrated that all but the weakest CQ, Guignard CQ, are too strong for a discussion of MPECs. Therefore, MPEC variants of all the standard CQs are introduced and investigated. A strongly stationary point (which is simply a KKT-point) is seen to be a necessary first order optimality condition only under the strongest CQs, MPEC-LICQ, MPEC-SMFCQ and Guignard CQ. Therefore a whole set of KKT-type conditions is investigated. A simple approach is given to acquire A-stationarity to be a necessary first order condition under MPEC-Guiganrd CQ. Finally, a whole chapter is devoted to investigating M-stationary, among the strongest stationarity concepts, second only to strong stationarity. It is shown to be a necessary first order condition under MPEC-Guignard CQ, the weakest known CQ for MPECs.

Level thesis:degree_level

thesis.doctoral

Grantor dc:publisher

Universität Würzburg

Year

2005

Author dc:creator

• Flegel, Michael L.

Contributors dc:contributor

• Kanzow, Christian

• MPEC
• MPCC
• M-Stationär
• Guignard CQ
• M-stationarity

Repository record source_url

https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/1068

OAI identifier oai:identifier

oai:opus.bibliothek.uni-wuerzburg.de:1068