On M-stationarity conditions in MPECs and the associated qualification conditions

dc.bibliographicCitation.seriesTitleWIAS Preprintseng
dc.bibliographicCitation.volume2215
dc.contributor.authorAdam, Lukáš
dc.contributor.authorHenrion, René
dc.contributor.authorOutrata, Jir̆í
dc.date.accessioned2016-12-13T10:46:55Z
dc.date.available2019-06-28T08:01:55Z
dc.date.issued2016
dc.description.abstractDepending on whether a mathematical program with equilibrium constraints (MPEC) is considered in its original or its enhanced (via KKT conditions) form, the assumed constraint qualifications (CQs) as well as the derived necessary optimality conditions may differ significantly. In this paper, we study this issue when imposing one of the weakest possible CQs, namely the calmness of the perturbation mapping associated with the respective generalized equations in both forms of the MPEC. It is well known that the calmness property allows one to derive socalled M-stationarity conditions. The strength of assumptions and conclusions in the two forms of the MPEC is strongly related with the CQs on the lower level imposed on the set whose normal cone appears in the generalized equation. For instance, under just the Mangasarian-Fromovitz CQ (a minimum assumption required for this set), the calmness properties of the original and the enhanced perturbation mapping are drastically different. They become identical in the case of a polyhedral set or when adding the Full Rank CQ. On the other hand, the resulting optimality conditions are affected too. If the considered set even satisfies the Linear Independence CQ, both the calmness assumption and the derived optimality conditions are fully equivalent for the original and the enhanced form of the MPEC. A compilation of practically relevant consequences of our analysis in the derivation of necessary optimality conditions is provided in the main Theorem 4.3. The obtained results are finally applied to MPECs with structured equilibria.eng
dc.description.versionpublishedVersioneng
dc.formatapplication/pdf
dc.identifier.issn2198-5855
dc.identifier.urihttps://doi.org/10.34657/2828
dc.identifier.urihttps://oa.tib.eu/renate/handle/123456789/1617
dc.language.isoengeng
dc.publisherBerlin : Weierstraß-Institut für Angewandte Analysis und Stochastikeng
dc.relation.issn0946-8633eng
dc.rights.licenseThis document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.eng
dc.rights.licenseDieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.ger
dc.subject.ddc510eng
dc.subject.otherMathematical programs with equilibrium constraintseng
dc.subject.otheroptimality conditionseng
dc.subject.otherconstraint qualificationeng
dc.subject.othercalmnesseng
dc.subject.otherperturbation mappingeng
dc.titleOn M-stationarity conditions in MPECs and the associated qualification conditionseng
dc.typeReporteng
dc.typeTexteng
tib.accessRightsopenAccesseng
wgl.contributorWIASeng
wgl.subjectMathematikeng
wgl.typeReport / Forschungsbericht / Arbeitspapiereng
Files
Original bundle
Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
86946762X.pdf
Size:
257.96 KB
Format:
Adobe Portable Document Format
Description: