Get Nichtlineare Optimierung: Neuere Verfahren Bibliographie PDF

By H.P. Künzi, W. Oettli, R. Pfranger, S.T. Tan

ISBN-10: 3540046429

ISBN-13: 9783540046424

ISBN-10: 3642951201

ISBN-13: 9783642951206

Das vorliegende Heft der Lecture Notes in Operations examine and Mathematical platforms verfolgt den Zweck, Interessenten der Nicht linearen Optimierung (Programmierung) mit einigen gangigen Algo rithrnen vertraut zu machen. Die Auswahl erhebt keinen Anspruch auf Vollstandigkeit, am ehesten konnte guy sie als Erganzung zu den in der II Nichtlinearen Programmierung" von KUnzi-Krelle-Oettli be schriebenen Methoden betrachten. Eine ausfUhrlichere und vollstandigere Darstellung wird einer Neu auflage des erwahnten Buches vorbehalten bleiben. Besonderes Gewicht im Sinne einer Materialsammlung legten wir auf die im Anschluss an die Verfahren beigefUgte Bibliographie der Nicht linearen Programmierung nebst ihren Grundlagen und Erweiterungen. Sie wird dem Leser die Moglichkeit geben, sich - auch unabhangig von der Sekundarliteratur - ein getreues Bild Uber den heutigen Stand dieser Theorie zu verschaffen. Eine derart ausfUhrliche Bestandesauf nahrne existierte unseres Wissens bisher nicht. Wir mochten noch darauf hinweisen, dass die einzelnen Kapitel durch gehend numeriert sind. FUr die Formelnumerierung wurden runde Klammern verwendet, eckige Klammern beziehen sich auf die am Schluss jedes Kapitels zitierten Arbeiten. Abschliessend mochten wir der Stiftung Volkswagenwerk in Hannover fUr den uns gewahrten Forschungskredit den herzlichsten Dank aus sprechen.

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Extra resources for Nichtlineare Optimierung: Neuere Verfahren Bibliographie

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Wir~ dass x ·optimal sei. 5. 4 OptimalWitskriterium: sN Beweis: = O. Aus der Definition (5. 8) von sN und sN o entnimmt man fUr die Nichtbasisvariablen: x. =- 0 ergibt v. = 0 1 1 0 ergibt v. z O. x. 2) erfilllt sind. Irn zweiten Fall~ x Da x 1 1 = sN" O~ versucht man in der Richtung s zu gehen: x +). s. ~ 0 gelten muss~ folgt 0 s A1 = min i=1~"1 n 1m Intervall 0 <: i\ s Funktion voni\. Dies ist N • s s A1 mit {- (5. 11) i\ 1 sucht man dann das Minimum von f als = v' ). moglich~ weil , (:N) . 12) N - 27 an der Stelle A= 0 gilt und f(x) stetig differenzierbar ist.

Somit gelten folgende Ungleichungen: Mit anderen Worten: Zu jedem t- Wert haben wir zwei das gesuchte~ Werte~ die endgilltige Minimum nach oben und unten begrenzen. Dies ergibt bei der praktischen Berechnung wertvolle Hinweise fUr das Abbrechen des Verfahrens. Bemerkungen: 1. Man kann ferner zeigen~ dass die Folgen monoton abnehmen. 2. Fur die Efficienz des Verfahrens ist die Wahl der Parameter rt wesentlich. rl darf zum Beispiel weder zu gross noch zu klein gewahlt werden. 51. Fur t ?! 2 wird meistens r t = r t-l /c gesetzt~ mit c > 1 konstant.

Damit ist aber p(x*.. r) = f(x*) = p(5t.. r) = f(5t). und x* ist optimal. Bemerkungen: fl ist nicht von vornherein bekannt. nach oben abgeschatzt werden.. falls ein Punkt xo.. x ° E ° C.. (x ) J -< 0.. j ~ J .. sowie eine untere Schranke S ... f(x) bekannt sind. Es sei nun p(x.. r) von der Form p(x.. r) = f(x) + r L. j ~ J [gJ:(X)] 2 oder in Vektornotation p(x.. r) = f(x) + r . [g +(x)] 2 fl. 5) gemachten Voraussetzungen fordern wir noch. 5) kompakt sei. Dann gilt Satz 4: Fur aile r > 0 existiert x{r) derart.

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Nichtlineare Optimierung: Neuere Verfahren Bibliographie by H.P. Künzi, W. Oettli, R. Pfranger, S.T. Tan


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