Degeneracy Graphs and the Neighbourhood Problem:
A few years ago nobody would have anticipated that in connection with degeneracy in Linear Programming quite a new field. could originate. In 1976 a very simple question has been posed: in the case an extreme pOint (EP) of a polytope is degenerate and the task is to find all neighbouring EP's...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1986
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| Ausgabe: | 1st ed. 1986 |
| Schriftenreihe: | Lecture Notes in Economics and Mathematical Systems
260 |
| Schlagworte: | |
| Online-Zugang: | BTU01 Volltext |
| Zusammenfassung: | A few years ago nobody would have anticipated that in connection with degeneracy in Linear Programming quite a new field. could originate. In 1976 a very simple question has been posed: in the case an extreme pOint (EP) of a polytope is degenerate and the task is to find all neighbouring EP's of the degenerate EP, is it necessary to determine all basic solutions of the corresponding equalities system associated with the degenerate EP -in order to be certain to determine all neighbours of this EP? This question implied another one: Does there exists a subset of the mentioned set of basic solutions such that it suffices to find such a subset in order to determine all neighbours? The first step to solve these questions (which are motivated in the first Chapter of this book) was to define a graph (called degeneracy graph) the nodes of which correspond to the basic solutions. It turned out that such a graph has some special properties and in order to solve the above questions firstly these properties had to be investigated. Also the structure of degeneracy graphs playes hereby an important role. Because the theory of degeneracy graphs was quite new, it was necessary to elaborate first a completely new terminology and to define new notions. Dr |
| Beschreibung: | 1 Online-Ressource (VIII, 132 p. 15 illus) |
| ISBN: | 9783642492709 |
| DOI: | 10.1007/978-3-642-49270-9 |
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| 245 | 1 | 0 | |a Degeneracy Graphs and the Neighbourhood Problem |c by H.-J. Kruse |
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| 520 | |a A few years ago nobody would have anticipated that in connection with degeneracy in Linear Programming quite a new field. could originate. In 1976 a very simple question has been posed: in the case an extreme pOint (EP) of a polytope is degenerate and the task is to find all neighbouring EP's of the degenerate EP, is it necessary to determine all basic solutions of the corresponding equalities system associated with the degenerate EP -in order to be certain to determine all neighbours of this EP? This question implied another one: Does there exists a subset of the mentioned set of basic solutions such that it suffices to find such a subset in order to determine all neighbours? The first step to solve these questions (which are motivated in the first Chapter of this book) was to define a graph (called degeneracy graph) the nodes of which correspond to the basic solutions. It turned out that such a graph has some special properties and in order to solve the above questions firstly these properties had to be investigated. Also the structure of degeneracy graphs playes hereby an important role. Because the theory of degeneracy graphs was quite new, it was necessary to elaborate first a completely new terminology and to define new notions. Dr | ||
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Datensatz im Suchindex
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| author | Kruse, H.-J |
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| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
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| edition | 1st ed. 1986 |
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| indexdate | 2024-07-10T08:56:07Z |
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| spelling | Kruse, H.-J. Verfasser aut Degeneracy Graphs and the Neighbourhood Problem by H.-J. Kruse 1st ed. 1986 Berlin, Heidelberg Springer Berlin Heidelberg 1986 1 Online-Ressource (VIII, 132 p. 15 illus) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Economics and Mathematical Systems 260 A few years ago nobody would have anticipated that in connection with degeneracy in Linear Programming quite a new field. could originate. In 1976 a very simple question has been posed: in the case an extreme pOint (EP) of a polytope is degenerate and the task is to find all neighbouring EP's of the degenerate EP, is it necessary to determine all basic solutions of the corresponding equalities system associated with the degenerate EP -in order to be certain to determine all neighbours of this EP? This question implied another one: Does there exists a subset of the mentioned set of basic solutions such that it suffices to find such a subset in order to determine all neighbours? The first step to solve these questions (which are motivated in the first Chapter of this book) was to define a graph (called degeneracy graph) the nodes of which correspond to the basic solutions. It turned out that such a graph has some special properties and in order to solve the above questions firstly these properties had to be investigated. Also the structure of degeneracy graphs playes hereby an important role. Because the theory of degeneracy graphs was quite new, it was necessary to elaborate first a completely new terminology and to define new notions. Dr Operations Research/Decision Theory Operations research Decision making Extremwert (DE-588)4137272-4 gnd rswk-swf Nachbarschaftsproblem (DE-588)4120782-8 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Graphentheorie (DE-588)4113782-6 gnd rswk-swf Entartungsgraph (DE-588)4121198-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Entartungsgraph (DE-588)4121198-4 s Nachbarschaftsproblem (DE-588)4120782-8 s DE-604 Extremwert (DE-588)4137272-4 s Lineare Optimierung (DE-588)4035816-1 s Graphentheorie (DE-588)4113782-6 s Erscheint auch als Druck-Ausgabe 9783540160496 Erscheint auch als Druck-Ausgabe 9783642492716 https://doi.org/10.1007/978-3-642-49270-9 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kruse, H.-J Degeneracy Graphs and the Neighbourhood Problem Operations Research/Decision Theory Operations research Decision making Extremwert (DE-588)4137272-4 gnd Nachbarschaftsproblem (DE-588)4120782-8 gnd Lineare Optimierung (DE-588)4035816-1 gnd Graphentheorie (DE-588)4113782-6 gnd Entartungsgraph (DE-588)4121198-4 gnd |
| subject_GND | (DE-588)4137272-4 (DE-588)4120782-8 (DE-588)4035816-1 (DE-588)4113782-6 (DE-588)4121198-4 (DE-588)4113937-9 |
| title | Degeneracy Graphs and the Neighbourhood Problem |
| title_auth | Degeneracy Graphs and the Neighbourhood Problem |
| title_exact_search | Degeneracy Graphs and the Neighbourhood Problem |
| title_exact_search_txtP | Degeneracy Graphs and the Neighbourhood Problem |
| title_full | Degeneracy Graphs and the Neighbourhood Problem by H.-J. Kruse |
| title_fullStr | Degeneracy Graphs and the Neighbourhood Problem by H.-J. Kruse |
| title_full_unstemmed | Degeneracy Graphs and the Neighbourhood Problem by H.-J. Kruse |
| title_short | Degeneracy Graphs and the Neighbourhood Problem |
| title_sort | degeneracy graphs and the neighbourhood problem |
| topic | Operations Research/Decision Theory Operations research Decision making Extremwert (DE-588)4137272-4 gnd Nachbarschaftsproblem (DE-588)4120782-8 gnd Lineare Optimierung (DE-588)4035816-1 gnd Graphentheorie (DE-588)4113782-6 gnd Entartungsgraph (DE-588)4121198-4 gnd |
| topic_facet | Operations Research/Decision Theory Operations research Decision making Extremwert Nachbarschaftsproblem Lineare Optimierung Graphentheorie Entartungsgraph Hochschulschrift |
| url | https://doi.org/10.1007/978-3-642-49270-9 |
| work_keys_str_mv | AT krusehj degeneracygraphsandtheneighbourhoodproblem |