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Numerische Verfahren zur Lösung nichtlinearer restringierter und unrestringierter Optimierungsaufgaben: Effizienz der numerischen Algorithmen by Dornes, Nadeshda

Numerische Verfahren zur Lösung nichtlinearer restringierter und unrestringierter Optimierungsaufgaben: Effizienz der numerischen Algorithmen

by Nadeshda Dornes
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Book cover type: Paperback
  • ISBN13: 9783958506633
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Diplomica Verlag
  • Publisher Imprint: Diplomica Verlag
  • Publication Date:
  • Pages: 120
  • Original Price: GBP 43.99
  • Language: German
  • Edition: N/A
  • Item Weight: 155 grams
  • BISAC Subject(s): General

Dieses Buch beschäftigt sich mit numerischen Verfahren zur Lösung nichtlinearer Optimierungsaufgaben. Grundlagen mehrerer Verfahren werden zu Beginn der Studie theoretisch formuliert und anschlie end auf Korrektheit und Effizienz untersucht. Das einleitende Kapitel stellt Definitionen und Sätze aus Optimierungstheorie, Linearer Algebra, Analysis und Numerik zusammen und erklärt Kriterien zur Konvergenzanalyse. Da sich die Lösung von drei der behandelten Verfahren auf die Lösung von sogenannten "unrestringierten" Problemen oder eines Gleichungssystems zurückführen lässt, wird zuerst ein Newton-artiges Verfahren vorgestellt. Dabei analysiert die Autorin wünschenswerte Eigenschaften, wie etwa globale Konvergenz und hohe Konvergenzordnung des Verfahrens. Im anschlie enden Kapitel stellt die Studie die sogenannten Penalty-, Penalty-Lagrange-, Barriere- und Innere-Punkte-Verfahren anhand der Hilfs-Funktionen mit den Algorithmen für eine numerische Behandlung vor und untersucht mithilfe der erstellten Konvergenzkriterien die verschiedenen Konvergenzeigenschaften. Den Schlusspunkt des Buches setzen numerische Fallstudien, wobei die Effizienz der Verfahren geprüft wird.

Nadeshda Dornes wurde 1984 in Russland geboren. Ihr Studium der Wirtschaftsmathematik an der Universität Ulm schloss die Autorin im Jahre 2013 mit dem akademischen Grad der Master of Science erfolgreich ab. Bereits während des Studiums sammelte die Autorin umfassende praktische Erfahrungen in der Finanzdienstleistungsbranche.

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