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Südwestdeutscher Verlag Für Hochschulschriften Die Innere-Punkte-Methode zur Lösung von Optimalsteuerproblemen: Theorie, Implementierung in Matlab und COMSOL Multiphysics, Beispiele

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Description

Die Innere-Punkte-Methode ist eine oft und erfolgreich angewandte Technik zur Lösung von restringierten Optimierungsaufgaben in endlichdimensionalen Vektorräumen. Hat man ein Optimierungsproblem mit partiellen Differentialgleichungen zu lösen, so muss dieses unendlichdimensionale Problem zuerst diskretisiert werden. Dabei geht die Struktur der partiellen Differentialgleichung in ein endlichdimensionales, nicht notwendigerweise lineares, Gleichungssystem auf. Will man jedoch die Struktur der Differentialgleichung nutzen, so bietet sich eine Übertragung der Innere-Punkte-Methode in eine Formulierung in (unendlichdimensionalen) Funktionenräumen an. Ausgehend von dem im Funktionenraum konstruierten Algorithmus wird eine Implementierung der Innere-Punkte-Methode vorgenommen. Dabei wird besonderer Wert auf die Integration schon vorhandener Software zur Lösung partieller Differentialgleichungen gelegt. Ein weiterer Aspekt bei der Implementierung der Innere-Punkte-Methode ist, inwieweit sich die Methode in bestehende Software integrieren lässt. Eine Reihe numerischer Beispiele bestätigt die theoretischen Konvergenzaussagen.

Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
09 August 2010
Listed Since
11 August 2010

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