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Klassifikation von Optimierungsproblemen

  • Lutz Gröll

    Lutz Gröll ist Gruppenleiter am Institut für Automation und angewandte Informatik (IAI) des Karlsruher Instituts für Technologie (KIT). Hauptarbeitsgebiete: Modellierung verfahrentstechnischer Anlagen, Identifikation, Systemtheorie und Regelungstechnik.

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Published/Copyright: November 8, 2018

Zusammenfassung

Der vorliegende Beitrag gibt einen Überblick zur Optimierung, wobei das Problem als solches und nicht die Algorithmen oder konkrete Anwendungen im Mittelpunkt stehen. Die Probleme werden eingeordnet, ihre Grundideen skizziert, und es werden Software-Tools zu ihrer Lösung genannt. Darüber hinaus diskutiert der Beitrag die Frage der Existenz und Eindeutigkeit von Lösungen für Optimierungsprobleme. Mit Hilfe erweiterter Ableitungskalküle werden notwendige Bedingungen für glatte und nichtglatte Zielfunktionen in endlich- und unendlichdimensionalen Räumen und auf Mannigfaltigkeiten formuliert. Diese mathematisch anspruchsvolleren Darstellungen richten sich an die in der Forschung tätigen Ingenieure.

Abstract

The present paper gives an overview of optimization where the main focus lies on the problem itself instead of the algorithms or practical applications. It arranges the problems, outlines their basic ideas, and names current software tools. Furthermore, the question of the existence and uniqueness of solutions to optimization problems is discussed. With the help of extended differential calculi, necessary conditions for smooth and non-smooth objective functions in finite and infinite dimensional spaces and on manifolds are obtained. These mathematically advanced considerations address engineers in research.

About the author

Lutz Gröll

Lutz Gröll ist Gruppenleiter am Institut für Automation und angewandte Informatik (IAI) des Karlsruher Instituts für Technologie (KIT). Hauptarbeitsgebiete: Modellierung verfahrentstechnischer Anlagen, Identifikation, Systemtheorie und Regelungstechnik.

Danksagung

Der Autor dankt Timm Faulwasser und Jörg Matthes für ein kritisches Lesen des Manuskripts und für zusätzliche Literaturhinweise. Ein besonderer Dank gilt Tessina Scholl für die schönen Bilder.

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Received: 2018-07-04
Accepted: 2018-10-01
Published Online: 2018-11-08
Published in Print: 2018-11-27

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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