Linear Programming Duality: An Introduction to Oriented Matroids
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1992
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The main theorem of Linear Programming Duality, relating a "primal" Linear Programming problem to its "dual" and vice versa, can be seen as a statement about sign patterns of vectors in complementary subspaces of Rn. This observation, first made by R.T. Rockafellar in the late sixties, 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 fundamental principles underlying Linear Programming 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 preferred to develop oriented matroids directly as appropriate abstractions of linear subspaces. Thus, the way we introduce oriented matroids 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 |
| Physical Description: | 1 Online-Ressource (IV, 216p. 40 illus) |
| ISBN: | 9783642581526 9783540554172 |
| ISSN: | 0172-5939 |
| DOI: | 10.1007/978-3-642-58152-6 |
Staff View
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| isbn | 9783642581526 9783540554172 |
| issn | 0172-5939 |
| language | English |
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| spelling | Bachem, Achim 1947- Verfasser (DE-588)170020185 aut Linear Programming Duality An Introduction to Oriented Matroids by Achim Bachem, Walter Kern Berlin, Heidelberg Springer Berlin Heidelberg 1992 1 Online-Ressource (IV, 216p. 40 illus) txt rdacontent c rdamedia cr rdacarrier Universitext 0172-5939 The main theorem of Linear Programming Duality, relating a "primal" Linear Programming problem to its "dual" and vice versa, can be seen as a statement about sign patterns of vectors in complementary subspaces of Rn. This observation, first made by R.T. Rockafellar in the late sixties, 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 fundamental principles underlying Linear Programming 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 preferred to develop oriented matroids directly as appropriate abstractions of linear subspaces. Thus, the way we introduce oriented matroids 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 Mathematics Mathematical optimization Economics Operations research Operations Research, Management Science Calculus of Variations and Optimal Control; Optimization Economic Theory Operation Research/Decision Theory Mathematik Wirtschaft Orientiertes Matroid (DE-588)4232299-6 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Dualität (DE-588)4013161-0 gnd rswk-swf Orientiertes Matroid (DE-588)4232299-6 s Lineare Optimierung (DE-588)4035816-1 s Dualität (DE-588)4013161-0 s 1\p DE-604 Kern, Walter 1957-2021 Sonstige (DE-588)13574850X oth https://doi.org/10.1007/978-3-642-58152-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bachem, Achim 1947- Linear Programming Duality An Introduction to Oriented Matroids Mathematics Mathematical optimization Economics Operations research Operations Research, Management Science Calculus of Variations and Optimal Control; Optimization Economic Theory Operation Research/Decision Theory Mathematik Wirtschaft Orientiertes Matroid (DE-588)4232299-6 gnd Lineare Optimierung (DE-588)4035816-1 gnd Dualität (DE-588)4013161-0 gnd |
| subject_GND | (DE-588)4232299-6 (DE-588)4035816-1 (DE-588)4013161-0 |
| title | Linear Programming Duality An Introduction to Oriented Matroids |
| title_auth | Linear Programming Duality An Introduction to Oriented Matroids |
| title_exact_search | Linear Programming Duality An Introduction to Oriented Matroids |
| title_full | Linear Programming Duality An Introduction to Oriented Matroids by Achim Bachem, Walter Kern |
| title_fullStr | Linear Programming Duality An Introduction to Oriented Matroids by Achim Bachem, Walter Kern |
| title_full_unstemmed | Linear Programming Duality An Introduction to Oriented Matroids by Achim Bachem, Walter Kern |
| title_short | Linear Programming Duality |
| title_sort | linear programming duality an introduction to oriented matroids |
| title_sub | An Introduction to Oriented Matroids |
| topic | Mathematics Mathematical optimization Economics Operations research Operations Research, Management Science Calculus of Variations and Optimal Control; Optimization Economic Theory Operation Research/Decision Theory Mathematik Wirtschaft Orientiertes Matroid (DE-588)4232299-6 gnd Lineare Optimierung (DE-588)4035816-1 gnd Dualität (DE-588)4013161-0 gnd |
| topic_facet | Mathematics Mathematical optimization Economics Operations research Operations Research, Management Science Calculus of Variations and Optimal Control; Optimization Economic Theory Operation Research/Decision Theory Mathematik Wirtschaft Orientiertes Matroid Lineare Optimierung Dualität |
| url | https://doi.org/10.1007/978-3-642-58152-6 |
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