Matthias Gerdts – författare

Das Operations Research befasst sich mit der Modellierung, qualitativen und quantitativen Analyse und algorithmischen Lösung von Entscheidungsproblemen. Es stellt Instrumente zur Analyse und Optimierung vernetzter Systemen bereit - u. a. in Wirtschaftsunternehmen, in der Städte- und Verkehrsplanung, Volkswirtschaft und Technik.

Es ist gleichermaßen Anwendungsfeld und Motivationsquelle für die in dieser Publikation behandelten Optimierungsverfahren.Deren Konzepte, theoretische Grundlagen und Eigenschaften werden ausführlich dargestellt. Zahlreiche Illustrationen unterstützen die Anschauung, viele vollständig durchgerechnete Beispiele tragen zum Verständnis bei und helfen beim Lösen der Übungsaufgaben. Das Buch richtet sich an Studierende mathematischer Studiengänge, aber auch an mathematisch interessierte Studierende ingenieur- und wirtschaftswissenschaftlicher Studiengänge sowie an Wissenschaftler aus den Bereichen Mathematik, Wirtschaftsmathematik, Technomathematik, Wirtschafts- und Ingenieurwissenschaften, die an einer Einführung in Theorie und Verfahren der Optimierung interessiert sind.

The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ordinary differential equations and differential-algebraic equations. An emphasis is placed on the interplay between the continuous optimal control problem, which typically is defined and analyzed in a Banach space setting, and discrete optimal control problems, which are obtained by discretization and lead to finite dimensional optimization problems.

The book addresses primarily master and PhD students as well as researchers in applied mathematics, but also engineers or scientists with a good background in mathematics and interest in optimal control. The theoretical parts of the book require some knowledge of functional analysis, the numerically oriented parts require knowledge from linear algebra and numerical analysis. Examples are provided for illustration purposes.

Ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) are widely used to model control systems in engineering, natural sciences, and economy. Optimal control plays a central role in optimizing such systems and to operate them effi ciently and safely. The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ODEs and DAEs. An emphasis is placed on the interplay between the optimal control problem, which typically is defi ned and analyzed in a Banach space setting, and discretizations thereof, which lead to finite dimensional optimization problems. The theoretical parts of the book require some knowledge of functional analysis, the numerically oriented parts require knowledge from linear algebra and numerical analysis. Practical examples are provided throughout the book for illustration purposes. The book addresses primarily master and PhD students as well as researchers in applied mathematics, but also engineers or scientists with a good background in mathematics. The book serves as a reference in research and teaching and hopefully helps to advance the state-of-the-art in optimal control.

Ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) are widely used to model control systems in engineering, natural sciences, and economy. Optimal control plays a central role in optimizing such systems and to operate them effi ciently and safely. The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ODEs and DAEs. An emphasis is placed on the interplay between the optimal control problem, which typically is defi ned and analyzed in a Banach space setting, and discretizations thereof, which lead to finite dimensional optimization problems. The theoretical parts of the book require some knowledge of functional analysis, the numerically oriented parts require knowledge from linear algebra and numerical analysis. Practical examples are provided throughout the book for illustration purposes. The book addresses primarily master and PhD students as well as researchers in applied mathematics, but also engineers or scientists with a good background in mathematics. The book serves as a reference in research and teaching and hopefully helps to advance the state-of-the-art in optimal control.