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Linear Programming Duality: An Introduction To Oriented Matroids - Achim Bachem
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Linear Programming Duality: An Introduction to Oriented Matroids - Achim Bachem, Walter Kern
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Achim Bachem, Walter Kern:
Linear Programming Duality: An Introduction to Oriented Matroids - neues Buch

ISBN: 9783540554172

ID: 978354055417

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. Achim Bachem, Walter Kern, Books, Business and Finance, Management and Leadership, Operations Research, Linear Programming Duality: An Introduction to Oriented Matroids Books>Business and Finance>Management and Leadership>Operations Research, Springer Berlin Heidelberg

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Linear Programming Duality - Achim Bachem
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Linear Programming Duality - neues Buch

ISBN: 9783540554172

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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. Bücher / Naturwissenschaften, Medizin, Informatik & Technik / Mathematik / Sonstiges, [PU: Springer, Berlin/Heidelberg]

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Linear Programming Duality: An Introduction to Oriented Matroids - Bachem, A. / Bachem, Achim / Kern, Walter
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Bachem, A. / Bachem, Achim / Kern, Walter:
Linear Programming Duality: An Introduction to Oriented Matroids - gebrauchtes Buch

ISBN: 9783540554172

ID: 7964751

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. Linear Programming Duality: An Introduction to Oriented Matroids Bachem, A. / Bachem, Achim / Kern, Walter, Springer

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Linear Programming Duality
Autor:

Bachem, Achim; Kern, Walter

Titel:

Linear Programming Duality

ISBN-Nummer:

3540554173

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.

Detailangaben zum Buch - Linear Programming Duality


EAN (ISBN-13): 9783540554172
ISBN (ISBN-10): 3540554173
Taschenbuch
Erscheinungsjahr: 1992
Herausgeber: Springer-Verlag GmbH
216 Seiten
Gewicht: 0,337 kg

Buch in der Datenbank seit 16.02.2007 21:09:56
Buch zuletzt gefunden am 25.10.2016 21:26:51
ISBN/EAN: 3540554173

ISBN - alternative Schreibweisen:
3-540-55417-3, 978-3-540-55417-2

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