Linear programming duality: an introduction to oriented matroids
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1992
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 216 S. graph. Darst. |
| ISBN: | 3540554173 0387554173 |
Internformat
MARC
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| 245 | 1 | 0 | |a Linear programming duality |b an introduction to oriented matroids |c Achim Bachem ; Walter Kern |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1992 | |
| 300 | |a 216 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
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| 650 | 4 | |a Dualität - Lineare Optimierung | |
| 650 | 4 | |a Orientiertes Matroid | |
| 650 | 4 | |a Linear programming | |
| 650 | 4 | |a Oriented matroids | |
| 650 | 0 | 7 | |a Orientiertes Matroid |0 (DE-588)4232299-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Dualität |0 (DE-588)4013161-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Optimierung |0 (DE-588)4035816-1 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-003407037 | ||
Datensatz im Suchindex
| _version_ | 1804119656076673024 |
|---|---|
| adam_text | Contents
1 Prerequisites 7
1.1 Sets and Relations 7
1.2 Linear Algebra 10
1.3 Topology 14
1.4 Polyhedra 15
2 Linear Duality in Graphs 19
2.1 Some Definitions 19
2.2 FARKAS Lemma for Graphs 22
2.3 Subspaces Associated with Graphs 24
2.4 Planar Graphs 32
2.5 Further Reading 35
3 Linear Duality and Optimization 37
3.1 Optimization Problems 37
3.2 Recognizing Optimal Solutions 40
3.3 Further Reading 43
4 The FARKAS Lemma 45
4.1 A first version 45
4.2 Homogenization 46
4.3 Linearization 49
4.4 Delinearization 51
4.5 Dehomogenization 53
4.6 Further Reading 54
5 Oriented Matroids 57
5.1 Sign Vectors 57
5.2 Minors 61
5.3 Oriented Matroids 63
5.4 Abstract Orthogonality 66
5.5 Abstract Elimination Property 67
5.6 Elementary vectors 70
!
4 CONTENTS
5.7 The Composition Theorem 73
5.8 Elimination Axioms 78
5.9 Approximation Axioms 78
5.10 Proof of FARKAS Lemma in OMs 81
5.11 Duality 83
5.12 Further Reading 83
6 Linear Programming Duality 89
6.1 The Dual Program 89
6.2 The Combinatorial Problem 94
6.3 Network Programming 107
6.4 Further Reading 110
7 Basic Facts in Polyhedral Theory 113
7.1 MlNKOWSKl s Theorem 114
7.2 Polarity 116
7.3 Faces of Polyhedral Cones 119
7.4 Faces and Interior Points 121
7.5 The Canonical Map 124
7.6 Lattices 127
7.7 Face Lattices of Polars 129
7.8 General Polyhedra 131
7.9 Further Reading 142
8 The Poset (O, ) 143
8.1 Simplifications 144
8.2 Basic Results 149
8.3 Shellability of Topes 156
8.4 Constructibility of O 164
8.5 Further Reading 169
9 Topological Realizations 171
9.1 Linear Sphere Systems 171
9.2 ANonUnearOM 174
9.3 Sphere Systems 176
9.4 PL Ball Complexes 183
9.5 Further Reading 195
|
| any_adam_object | 1 |
| author | Bachem, Achim 1947- Kern, Walter 1957-2021 |
| author_GND | (DE-588)170020185 (DE-588)13574850X |
| author_facet | Bachem, Achim 1947- Kern, Walter 1957-2021 |
| author_role | aut aut |
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| building | Verbundindex |
| bvnumber | BV005445359 |
| callnumber-first | Q - Science |
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| callnumber-search | QA166.6 |
| callnumber-sort | QA 3166.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 870 SK 890 |
| classification_tum | MAT 912f MAT 052f |
| ctrlnum | (OCoLC)246888024 (DE-599)BVBBV005445359 |
| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005445359 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:29:39Z |
| institution | BVB |
| isbn | 3540554173 0387554173 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003407037 |
| oclc_num | 246888024 |
| open_access_boolean | |
| owner | DE-384 DE-739 DE-91G DE-BY-TUM DE-824 DE-29T DE-355 DE-BY-UBR DE-20 DE-706 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-384 DE-739 DE-91G DE-BY-TUM DE-824 DE-29T DE-355 DE-BY-UBR DE-20 DE-706 DE-634 DE-83 DE-11 DE-188 |
| physical | 216 S. graph. Darst. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Bachem, Achim 1947- Verfasser (DE-588)170020185 aut Linear programming duality an introduction to oriented matroids Achim Bachem ; Walter Kern Berlin u.a. Springer 1992 216 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Dualität - Lineare Optimierung Orientiertes Matroid Linear programming Oriented matroids Orientiertes Matroid (DE-588)4232299-6 gnd rswk-swf Dualität (DE-588)4013161-0 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Orientiertes Matroid (DE-588)4232299-6 s Lineare Optimierung (DE-588)4035816-1 s Dualität (DE-588)4013161-0 s DE-604 Kern, Walter 1957-2021 Verfasser (DE-588)13574850X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003407037&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bachem, Achim 1947- Kern, Walter 1957-2021 Linear programming duality an introduction to oriented matroids Dualität - Lineare Optimierung Orientiertes Matroid Linear programming Oriented matroids Orientiertes Matroid (DE-588)4232299-6 gnd Dualität (DE-588)4013161-0 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4232299-6 (DE-588)4013161-0 (DE-588)4035816-1 |
| 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 Achim Bachem ; Walter Kern |
| title_fullStr | Linear programming duality an introduction to oriented matroids Achim Bachem ; Walter Kern |
| title_full_unstemmed | Linear programming duality an introduction to oriented matroids 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 | Dualität - Lineare Optimierung Orientiertes Matroid Linear programming Oriented matroids Orientiertes Matroid (DE-588)4232299-6 gnd Dualität (DE-588)4013161-0 gnd Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Dualität - Lineare Optimierung Orientiertes Matroid Linear programming Oriented matroids Dualität Lineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003407037&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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