Lineare und Netzwerk-Optimierung / Linear and by Prof. Dr. Horst W. Hamacher, Prof. Dr. Kathrin Klamroth

By Prof. Dr. Horst W. Hamacher, Prof. Dr. Kathrin Klamroth (auth.)

Ziel des Buches ist es, Grundlagen der Linearen Optimierung einzuf?hren und einige der klassischen polynomial l?sbaren Netzwerkprobleme vorzustellen. Das Besondere dieses Lehrbuches ist die Tatsache, dass die Textteile parallel auf Deutsch und Englisch formuliert wurden, so dass neben der Vermittlung des Grundwissens in mathematischer Optimierung auch eine Einf?hrung ins Fachenglisch bzw. in die deutsche Sprache stattfindet.
The ebook is geared in the direction of a uncomplicated knowing of the thoughts of linear optimization and of a few vintage, polynomially solvable community optimization difficulties. the original characteristic of this booklet is that the verbal components were formulated either in German and English. during this approach instructing of simple wisdom in mathematical optimization will be mixed with an advent into English as technical language or into the German language.

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Hat man eine zulässige Basislösung gefunden, so heißt die anschließende Minimierung der ursprünglichen Zielfunktion die 2. Phase des Simplexverfahrens. Bei der praktischen Durchführung beachte man folgendes: The minimization of the auxiliary objective function h({f) is called phase 1 of the Simplex Method. Once a basic feasible solution is found, the consecutive minimization of the original objective function is called phase 2 of the Simplex Method. In practical applications of this method remember that: (1) Man darf nicht vergessen, im Starttableau in den zu künstlichen Variablen gehörenden Spalten Einheitsvektoren zu bilden.

AB(m») eine reguläre Teilmatrix von A ist. Ist L u U eine Partition von N = {I, ... h. As in the case of unbounded variables, a basis B = (B(l), ... ), . , AB(m») is a non-singular submatrix of A. If LuU is a partition of N = {I, ... e. LUU=N and LnU= 0, and if also U n J = so läßt sich jede Lösung ± von A± = Q in der folgenden Basisdarstellung bzgl. 7) ± mit (±B, ±L' hJ) heißt Basislösung bzgl. - {Loj if jELnJ if jE Ln J V JEU V JE L Dabei nennen wir Xj, j E B Basisvariable, Xj, j E L uS-Nichtbasisvariable ("untere Schranke") und Xj, JEU oSNichtbasisvariable ("obere Schranke").

I, 3, 5}, -D A starting solution is given by B {I, 3, 5}, L = {2} and U = {4}. Tl>' •. Tm) = fBAB 1 play a central role in this section. 1 implies that B is an optimal basis of the LP spielen in diesem Abschnitt eine große Rolle. 1) wissen wir, dass B eine optimale Basis des LP (P) 1[ min{f~ : A~ = Q, ~ 2: Q} ist, falls Cj = Cj -1[Aj 2: 0 V JEN.

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