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Linear Programming Duality
An Introduction to Oriented Matroids, Universitext
ISBN/EAN: 9783540554172
Umbreit-Nr.: 1470095
Sprache:
Englisch
Umfang: iv, 218 S.
Format in cm:
Einband:
kartoniertes Buch
Erschienen am 30.07.1992
- Zusatztext
- 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.
- Kurztext
- Linear Programming Duality is one of the cornerstones in combinatorial optimization. Giving an elementary introduction to the theory of oriented matroids, this book presents an approach which clarifies the theoretical basis of linear programming and also simplifies the proofs of standard results.