Constraint Qualifications Und Optimalitatsbedingungen Fur Mpecs (German Edition) Book PDF, ePub eBook

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Book Descriptions:
Diplomarbeit aus dem Jahr 2009 im Fachbereich Mathematik - Angewandte Mathematik, Note: 1,0, Universität Regensburg, Sprache: Deutsch, Anmerkungen: Mathematical program with equilibrium constraints [MPEC], Nonlinear Program [NLP], tangent cones, Constraint qualifications, Guignard Constraint Qualification, Adabie Constraint Qualification, Boulingard stationarity, A-, C-, M-, S-stationarity, SPQ-methods, inner point methods, SLPEC-EQP , Abstract: Der Schwerpunkt dieser Diplomarbeit liegt in der theoretischen Analyse eines mathematical programs with equilibrium constraints [MPEC]. Inspiriert durch Arbeiten von Kanzow und Flegel ([2], [4], [5]) werden die Tangentialkegel des MPEC und seiner Hilfsproble- me, sowie deren Zusammenhänge betrachtet. Ausgehend von diesem geometrischen Standpunkt werden geometrische Constraint Qualifications [CQ] eingeführt, welche sicherstellen, dass die jeweils linearisierten Tangentialkegel die tatsächliche Beschaffenheit des zulässigen Bereichs auch richtig beschreiben. Eine wesentliche Rolle spielt dabei die lange Zeit in Vergessenheit geratene Guignard Constraint Qualification [GCQ]. Mit der GCQ stellen wir eine schwache nicht MPEC-spezifische CQ vor, welche für eine große Klasse von MPECs erfüllt werden kann. Mit der MPEC-GCQ definieren wir die bisher schwächste CQ speziell für MPECs. Auf Basis dieser CQs werden sowohl geometrische Optimalitätsbedingungen, wie die Boulingard - Stationarität, als auch Optimalitätsbedingungen vom KKT-Typ (A-, C-, M-, S-Stationarität) hergeleitet. Neben diesen notwendigen Bedingungen erster Ordnung wird mit der MPEC-WSOSC auch eine neue hinreichende Optimalitätsbedingung definiert, welche keinen stark stationären Punkt voraussetzt. In einem weiteren Schritt wird die Anwendung dieser Theorie auf eine engere Auswahl an Lösern für MPECs besprochen.

Constraint Qualifications Und Optimalitatsbedingungen Fur Mpecs (German Edition) by Michael Schinabeck

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