Linear Programming Duality: An Introduction To Oriented Matroids (Universitext) - Softcover

Bachem, Achim

 
9783540554172: Linear Programming Duality: An Introduction To Oriented Matroids (Universitext)
Softcover
ISBN 10: 3540554173 ISBN 13: 9783540554172
Verlag: Springer, 2013

Inhaltsangabe

The main theorem of Linear Programming Duality, relating a "pri­ mal" Linear Programming problem to its "dual" and vice versa, can be seen as a statement about sign patterns of vectors in complemen­ tary subspaces of Rn. This observation, first made by R.T. Rockafellar in the late six­ ties, led to the introduction of certain systems of sign vectors, called "oriented matroids". Indeed, when oriented matroids came into being in the early seventies, one of the main issues was to study the fun­ damental principles underlying Linear Progra.mrning Duality in this abstract setting. In the present book we tried to follow this approach, i.e., rather than starting out from ordinary (unoriented) matroid theory, we pre­ ferred to develop oriented matroids directly as appropriate abstrac­ tions of linear subspaces. Thus, the way we introduce oriented ma­ troids makes clear that these structures are the most general -and hence, the most simple -ones in which Linear Programming Duality results can be stated and proved. We hope that this helps to get a better understanding of LP-Duality for those who have learned about it before und a good introduction for those who have not.

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Reseña del editor

The main theorem of Linear Programming Duality, relating a "pri­ mal" Linear Programming problem to its "dual" and vice versa, can be seen as a statement about sign patterns of vectors in complemen­ tary subspaces of Rn. This observation, first made by R.T. Rockafellar in the late six­ ties, led to the introduction of certain systems of sign vectors, called "oriented matroids". Indeed, when oriented matroids came into being in the early seventies, one of the main issues was to study the fun­ damental principles underlying Linear Progra.mrning Duality in this abstract setting. In the present book we tried to follow this approach, i.e., rather than starting out from ordinary (unoriented) matroid theory, we pre­ ferred to develop oriented matroids directly as appropriate abstrac­ tions of linear subspaces. Thus, the way we introduce oriented ma­ troids makes clear that these structures are the most general -and hence, the most simple -ones in which Linear Programming Duality results can be stated and proved. We hope that this helps to get a better understanding of LP-Duality for those who have learned about it before und a good introduction for those who have not.

Reseña del editor

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

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Verlag
Springer
Erscheinungsdatum
2013
Sprache
Englisch
ISBN 10 
3540554173
ISBN 13 
9783540554172
Einband
Tapa blanda
Anzahl der Seiten
224
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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Hamburg
Deutschland

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9780387554174: Linear Programming Duality: An Introduction to Oriented Matroids (Universitext)

Vorgestellte Ausgabe

ISBN 10:  0387554173 ISBN 13:  9780387554174
Softcover