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Optimierung pp 387–430Cite as

Numerische Verfahren für dynamische Optimierungsprobleme

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Zusammenfassung

Die in den Kap. 10, 11 und 13 abgeleiteten notwendigen Optimalitätsbedingungen erlauben die analytische Lösung bestimmter Klassen von dynamischen Optimierungsproblemen. So hat man beispielsweise in Kap. 12 für Probleme mit LQ-Struktur und beliebigen Dimensionen optimale Steuer- und Regelgesetze ableiten können. Ebenso ist uns in Kap. 11 sowie bei einer Reihe von Beispielen und Übungen eine analytische Lösung kleindimensionaler Probleme gelungen. Außer der analytischen Behandlung dynamischer Optimierungsprobleme wurde in Kap. 14 aus dem Optimalitätsprinzip das numerische Verfahren der diskreten dynamischen Programmierung entwickelt. Wie wir gesehen haben, eignet sich dieses Verfahren zwar prinzipiell zur numerischen Lösung dynamischer Problemstellungen unter vielfältigen Nebenbedingungen, durch den exponentiell wachsenden rechentechnischen Aufwand wird aber sein praktischer Einsatzbereich bei wachsenden Problemdimensionen stark eingeschränkt. Es ist das Ziel dieses Kapitels, weitere numerische Verfahren für dynamische Optimierungsprobleme vorzustellen, die uns erlauben, die Optimierungstheorie bei einer Reihe von praktisch bedeutungsvollen Aufgabenstellungen (auch höherer Dimensionen) erfolgreich einzusetzen.

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Author information

Authors and Affiliations

  1. Technical University of Crete, Chania, Griechenland

    Markos Papageorgiou

  2. TU München, München, Deutschland

    Marion Leibold

  3. TU München, München, Deutschland

    Martin Buss

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  1. Markos Papageorgiou
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  2. Marion Leibold
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  3. Martin Buss
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Correspondence to Markos Papageorgiou .

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Papageorgiou, M., Leibold, M., Buss, M. (2015). Numerische Verfahren für dynamische Optimierungsprobleme. In: Optimierung. Springer Vieweg, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46936-1_15

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  • DOI: https://doi.org/10.1007/978-3-662-46936-1_15

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