Constraint qualifications and stationarity concepts for mathematical programs with equilibrium constraints
Regularitätsbedingungen und Stationaritätskonzepte für Mathematische Programme mit Gleichgewichtsnebenbedingungen
Please always quote using this URN: urn:nbn:de:bvb:20-opus-12453
- 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 wholeAn 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.…
| Author: | Michael L. Flegel |
|---|---|
| URN: | urn:nbn:de:bvb:20-opus-12453 |
| Document Type: | Doctoral Thesis |
| Granting Institution: | Universität Würzburg, Fakultät für Mathematik und Informatik |
| Faculties: | Fakultät für Mathematik und Informatik / Institut für Mathematik |
| Date of final exam: | 2005/03/11 |
| Language: | English |
| Year of Completion: | 2005 |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| GND Keyword: | Nichtlineare Optimierung |
| Tag: | Guignard CQ; M-Stationär; MPCC; MPEC Guignard CQ; M-stationarity; MPCC; MPEC |
| MSC-Classification: | 49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J53 Set-valued and variational analysis [See also 28B20, 47H04, 54C60, 58C06] |
| Release Date: | 2005/04/04 |
| Advisor: | Prof. Dr. Christian Kanzow |