In-Depth Analysis of Linear Programming:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2001
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Along with the traditional material concerning linear programming (the simplex method, the theory of duality, the dual simplex method), In-Depth Analysis of Linear Programming contains new results of research carried out by the authors. For the first time, the criteria of stability (in the geometrical and algebraic forms) of the general linear programming problem are formulated and proved. New regularization methods based on the idea of extension of an admissible set are proposed for solving unstable (ill-posed) linear programming problems. In contrast to the well-known regularization methods, in the methods proposed in this book the initial unstable problem is replaced by a new stable auxiliary problem. This is also a linear programming problem, which can be solved by standard finite methods. In addition, the authors indicate the conditions imposed on the parameters of the auxiliary problem which guarantee its stability, and this circumstance advantageously distinguishes the regularization methods proposed in this book from the existing methods. In these existing methods, the stability of the auxiliary problem is usually only presupposed but is not explicitly investigated. In this book, the traditional material contained in the first three chapters is expounded in much simpler terms than in the majority of books on linear programming, which makes it accessible to beginners as well as those more familiar with the area |
| Beschreibung: | 1 Online-Ressource (XIV, 312 p) |
| ISBN: | 9789401597593 9789048158515 |
| DOI: | 10.1007/978-94-015-9759-3 |
Internformat
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| 500 | |a Along with the traditional material concerning linear programming (the simplex method, the theory of duality, the dual simplex method), In-Depth Analysis of Linear Programming contains new results of research carried out by the authors. For the first time, the criteria of stability (in the geometrical and algebraic forms) of the general linear programming problem are formulated and proved. New regularization methods based on the idea of extension of an admissible set are proposed for solving unstable (ill-posed) linear programming problems. In contrast to the well-known regularization methods, in the methods proposed in this book the initial unstable problem is replaced by a new stable auxiliary problem. This is also a linear programming problem, which can be solved by standard finite methods. In addition, the authors indicate the conditions imposed on the parameters of the auxiliary problem which guarantee its stability, and this circumstance advantageously distinguishes the regularization methods proposed in this book from the existing methods. In these existing methods, the stability of the auxiliary problem is usually only presupposed but is not explicitly investigated. In this book, the traditional material contained in the first three chapters is expounded in much simpler terms than in the majority of books on linear programming, which makes it accessible to beginners as well as those more familiar with the area | ||
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Datensatz im Suchindex
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| author | Vasilyev, F. P. |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9759-3 |
| format | Electronic eBook |
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| id | DE-604.BV042424164 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:15Z |
| institution | BVB |
| isbn | 9789401597593 9789048158515 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859581 |
| oclc_num | 864069743 |
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| spelling | Vasilyev, F. P. Verfasser aut In-Depth Analysis of Linear Programming by F. P. Vasilyev, A. Yu. Ivanitskiy Dordrecht Springer Netherlands 2001 1 Online-Ressource (XIV, 312 p) txt rdacontent c rdamedia cr rdacarrier Along with the traditional material concerning linear programming (the simplex method, the theory of duality, the dual simplex method), In-Depth Analysis of Linear Programming contains new results of research carried out by the authors. For the first time, the criteria of stability (in the geometrical and algebraic forms) of the general linear programming problem are formulated and proved. New regularization methods based on the idea of extension of an admissible set are proposed for solving unstable (ill-posed) linear programming problems. In contrast to the well-known regularization methods, in the methods proposed in this book the initial unstable problem is replaced by a new stable auxiliary problem. This is also a linear programming problem, which can be solved by standard finite methods. In addition, the authors indicate the conditions imposed on the parameters of the auxiliary problem which guarantee its stability, and this circumstance advantageously distinguishes the regularization methods proposed in this book from the existing methods. In these existing methods, the stability of the auxiliary problem is usually only presupposed but is not explicitly investigated. In this book, the traditional material contained in the first three chapters is expounded in much simpler terms than in the majority of books on linear programming, which makes it accessible to beginners as well as those more familiar with the area Mathematics Information theory Computer science / Mathematics Mathematical optimization Economics Optimization Computational Mathematics and Numerical Analysis Economic Theory Operations Research, Management Science Theory of Computation Informatik Mathematik Wirtschaft Lineare Optimierung (DE-588)4035816-1 gnd rswk-swf Lineare Optimierung (DE-588)4035816-1 s 1\p DE-604 Ivanitskiy, A. Yu Sonstige oth https://doi.org/10.1007/978-94-015-9759-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Vasilyev, F. P. In-Depth Analysis of Linear Programming Mathematics Information theory Computer science / Mathematics Mathematical optimization Economics Optimization Computational Mathematics and Numerical Analysis Economic Theory Operations Research, Management Science Theory of Computation Informatik Mathematik Wirtschaft Lineare Optimierung (DE-588)4035816-1 gnd |
| subject_GND | (DE-588)4035816-1 |
| title | In-Depth Analysis of Linear Programming |
| title_auth | In-Depth Analysis of Linear Programming |
| title_exact_search | In-Depth Analysis of Linear Programming |
| title_full | In-Depth Analysis of Linear Programming by F. P. Vasilyev, A. Yu. Ivanitskiy |
| title_fullStr | In-Depth Analysis of Linear Programming by F. P. Vasilyev, A. Yu. Ivanitskiy |
| title_full_unstemmed | In-Depth Analysis of Linear Programming by F. P. Vasilyev, A. Yu. Ivanitskiy |
| title_short | In-Depth Analysis of Linear Programming |
| title_sort | in depth analysis of linear programming |
| topic | Mathematics Information theory Computer science / Mathematics Mathematical optimization Economics Optimization Computational Mathematics and Numerical Analysis Economic Theory Operations Research, Management Science Theory of Computation Informatik Mathematik Wirtschaft Lineare Optimierung (DE-588)4035816-1 gnd |
| topic_facet | Mathematics Information theory Computer science / Mathematics Mathematical optimization Economics Optimization Computational Mathematics and Numerical Analysis Economic Theory Operations Research, Management Science Theory of Computation Informatik Mathematik Wirtschaft Lineare Optimierung |
| url | https://doi.org/10.1007/978-94-015-9759-3 |
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