Linear Programming Duality : An Introduction to Oriented Matroids
Bachem, Achim and Kern, Walter (1992) Linear Programming Duality : An Introduction to Oriented Matroids. Universitext . Springer, Berlin .
Abstract
This book presents an elementary introduction to the theory of oriented matroids. The way oriented matroids are introduced 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 with results on polyhedra in R n and show how to restate the essence of the proofs in terms of sign patterns of oriented matroids. 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 further reading and the references provide an overview of the research in this field.
Item Type:  Book, Conference volume, Special Journal issue 

Citations:  67 (Google Scholar)  
Uncontrolled Keywords:  duality Farkas lemma oriented matroids partially ordered sets polyhedra 
Subjects: 

Divisions:  Mathematical Institute 
Related URLs: 
ZAIK Number:  zpr89074 

Depositing User:  Archive Admin 
Date Deposited:  02 Apr 2001 00:00 
Last Modified:  21 Oct 2011 13:42 
URI:  http://earchive.informatik.unikoeln.de/id/eprint/74 