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Zwei Lösungsmethoden Für Nichtkonvexe Programmierungsprobleme by U. Ueing

Zwei Lösungsmethoden Für Nichtkonvexe Programmierungsprobleme

by U. Ueing
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Book cover type: Paperback
  • ISBN13: 9783540054153
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 96
  • Original Price: EUR 51.39
  • Language: German
  • Edition: N/A
  • Item Weight: 186 grams
  • BISAC Subject(s): Economics / General

Programmierungen sind ein sehr wirkungsvolles Instrument zur prak- tischen Berechnung optimaler wirtschaftlicher Entscheidungen. 1m ein- fachsten Fall der linearen Programmierung wird eine lipeare Zielfunk- tion bei Geltung linearer Ungleichungen als Nebenbedingung maximiert oder minimiert. Sehr viele 6konomische Probleme lassen sich in diese Form bringen. Leider ist das nicht bei allen m6glich: sehr wichtige Probleme (z. E. viele Investitionsprobleme) fUhren auf nichtlineare Zielfunktionen und nichtlinear-e Ungleichungen als Nebenbedingungen. Es gibt in der Zwischenzeit eine ganze Reihe von Rechenverfahren, die ge- statten, von einem beliebigen, zul ssigen Anfangspunkt ausgehend ite- rativ ein lokales Extremum zu berechnen. Leider liegen die Probleme h ufig so, daE zahlreiche lokale Extrema existieren, w hrend man natUr- lich am globalen Extremum interessiert ist. Bisher hat es nur ein Ver- fahren gegeben (das von Orden und Ritter), das fUr einen Spezialfall quadrati scher Formen als Zielfunktion und fUr lineare Ungleichungen als Nebenbedingungen das globale Extrumum in endlich vie len Rechenschritten zu erreichen gestattet. Alle Versuche zur Verallgemeinerung dieses Ver- fahrens auf beliebige nichtlineare Zielfunktionen oder nichtlineare Ne- benbedingungen sind bisher gescheitert. Hier setzt nun die Arbeit von Herrn Ueing ein. Er entwickelt zwei Ver- fahren, die mit tragbarem Rechenaufwand von einem lokalen Extremum zum n chsten mit einem h6heren Wert der Zielfunktion (bei einer Maximumauf- gabe) Uberzugehen gestatten. Das erste Verfahren, dessen allgemeine Idee von mir schon vor einiger Zeit vorgeschlagen wurde. ist sehr allgemein: es verlangt fast keine Einschr nkungen der Zielfunktionen und der Neben- bedingungen.

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