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Linear Programming Duality - Achim Bachem, Walter Kern
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Linear Programming Duality - nouveau livre

1992, ISBN: 3540554173

Der Begriff der Dualität in der linearen Programmierung ist von zentraler Bedeutung in der kombinatorischen Optimierung. Beide Autoren haben viele Jahre auf diesem Gebiet gearbeitet. Sie … Plus…

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Linear Programming Duality: An Introduction To Oriented Matroids (Universitext) - Bachem, Achim
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Linear Programming Duality: An Introduction To Oriented Matroids (Universitext) - Livres de poche

2013, ISBN: 9783540554172

Springer, Taschenbuch, Auflage: 1992, 224 Seiten, Publiziert: 2013-10-04T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: 40 black & white illustrations, 0.72 kg, Recht, Kategorien, Bücher… Plus…

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1992

ISBN: 9783540554172

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Linear Programming Duality - Achim Bachem/ Walter Kern
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Linear Programming Duality

This book presents an elementary introduction to the theoryof oriented matroids. The way oriented matroids are intro-duced emphasizes that they are the most general - and hencesimplest - structures for which linear Programming Dualityresults can be stated and proved. The main theme of the bookis duality.Using Farkas' Lemma as the basis the authors start withre-sults on polyhedra in Rn and show how to restate the essenceof the proofs in terms of sign patterns of oriented ma-troids. Most of the standard material in Linear Programmingis presented in the setting of real space as well as in themore abstract theory of oriented matroids. This approachclarifies the theory behind Linear Programming and proofsbecome simpler.The last part of the book deals with the facial structure ofpolytopes respectively their oriented matroid counterparts.It is an introduction to more advanced topics in orientedmatroid theory. Each chapter contains suggestions for furt-herreading and the references provide an overview of theresearch in this field.

Informations détaillées sur le livre - Linear Programming Duality


EAN (ISBN-13): 9783540554172
ISBN (ISBN-10): 3540554173
Livre de poche
Date de parution: 1992
Editeur: Springer Berlin Heidelberg
216 Pages
Poids: 0,337 kg

Livre dans la base de données depuis 2007-02-16T21:09:56+01:00 (Zurich)
Page de détail modifiée en dernier sur 2024-03-11T17:44:17+01:00 (Zurich)
ISBN/EAN: 3540554173

ISBN - Autres types d'écriture:
3-540-55417-3, 978-3-540-55417-2
Autres types d'écriture et termes associés:
Auteur du livre: walter kern, bachem, stock, university twente
Titre du livre: introduction, duality, linear programming, matroid, oriented matroids, walter kern, englisch berlin


Données de l'éditeur

Auteur: Achim Bachem; Walter Kern
Titre: Universitext; Linear Programming Duality - An Introduction to Oriented Matroids
Editeur: Springer; Springer Berlin
218 Pages
Date de parution: 1992-07-30
Berlin; Heidelberg; DE
Langue: Anglais
96,29 € (DE)
98,99 € (AT)
106,50 CHF (CH)
Available
IV, 218 p.

BC; Hardcover, Softcover / Mathematik/Sonstiges; Unternehmensforschung; Verstehen; Algebra; Linear Programming Duality; Lineare Optimierungsdualität; Oriented Matroids; Orientierte Matroide; Polyedertheorie; Polyhedral Theory; linear algebra; linear optimization; Operations Research, Management Science; Algebra; Econometrics; Calculus of Variations and Optimization; Quantitative Economics; Operations Research and Decision Theory; Algebra; Ökonometrie und Wirtschaftsstatistik; Optimierung; Wirtschaftstheorie und -philosophie; Management: Entscheidungstheorie; EA

1 Prerequisites.- 7.1 Sets and Relations.- 10.2 Linear Algebra.- 14.3 Topology.- 15.4 Polyhedra.- 2 Linear Duality in Graphs.- 2.1 Some Definitions.- 2.2 FARKAS’ Lemma for Graphs.- 2.3 Subspaces Associated with Graphs.- 2.4 Planar Graphs.- 2.5 Further Reading.- 3 Linear Duality and Optimization.- 3.1 Optimization Problems.- 3.2 Recognizing Optimal Solutions.- 3.3 Further Reading.- 4 The FARKAS Lemma.- 4.1 A first version.- 4.2 Homogenization.- 4.3 Linearization.- 4.4 Delinearization.- 4.5 Dehomogenization.- 4.6 Further Reading.- 5 Oriented Matroids.- 5.1 Sign Vectors.- 5.2 Minors.- 5.3 Oriented Matroids.- 5.4 Abstract Orthogonality.- 5.5 Abstract Elimination Property.- 5.6 Elementary vectors.- 5.7 The Composition Theorem.- 5.8 Elimination Axioms.- 5.9 Approximation Axioms.- 5.10 Proof of FARKAS’ Lemma in OMs.- 5.11 Duality.- 5.12 Further Reading.- 6 Linear Programming Duality.- 6.1 The Dual Program.- 6.2 The Combinatorial Problem.- 6.3 Network Programming.- 6.4 Further Reading.- 7 Basic Facts in Polyhedral Theory.- 7.1 MINKOWSKI’S Theorem.- 7.2 Polarity.- 7.3 Faces of Polyhedral Cones.- 7.4 Faces and Interior Points.- 7.5 The Canonical Map.- 7.6 Lattices.- 7.7 Face Lattices of Polars.- 7.8 General Polyhedra.- 7.9 Further Reading.- 8 The Poset (O, ?).- 8.1 Simplifications.- 8.2 Basic Results.- 8.3 Shellability of Topes.- 8.4 Constructibility of O.- 8.5 Further Reading.- 9 Topological Realizations.- 9.1 Linear Sphere Systems.- 9.2 A Nonlinear OM.- 9.3 Sphere Systems.- 9.4 PL Ball Complexes.- 9.5 Further Reading.

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