Large-scale Optimization — Problems and Methods:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2001
|
| Schriftenreihe: | Applied Optimization
51 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control |
| Beschreibung: | 1 Online-Ressource (XII, 312 p) |
| ISBN: | 9781475732436 9781441948489 |
| ISSN: | 1384-6485 |
| DOI: | 10.1007/978-1-4757-3243-6 |
Internformat
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-3243-6 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:09Z |
| institution | BVB |
| isbn | 9781475732436 9781441948489 |
| issn | 1384-6485 |
| language | English |
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| physical | 1 Online-Ressource (XII, 312 p) |
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| spelling | Tsurkov, Vladimir Verfasser aut Large-scale Optimization — Problems and Methods by Vladimir Tsurkov Boston, MA Springer US 2001 1 Online-Ressource (XII, 312 p) txt rdacontent c rdamedia cr rdacarrier Applied Optimization 51 1384-6485 Decomposition methods aim to reduce large-scale problems to simpler problems. This monograph presents selected aspects of the dimension-reduction problem. Exact and approximate aggregations of multidimensional systems are developed and from a known model of input-output balance, aggregation methods are categorized. The issues of loss of accuracy, recovery of original variables (disaggregation), and compatibility conditions are analyzed in detail. The method of iterative aggregation in large-scale problems is studied. For fixed weights, successively simpler aggregated problems are solved and the convergence of their solution to that of the original problem is analyzed. An introduction to block integer programming is considered. Duality theory, which is widely used in continuous block programming, does not work for the integer problem. A survey of alternative methods is presented and special attention is given to combined methods of decomposition. Block problems in which the coupling variables do not enter the binding constraints are studied. These models are worthwhile because they permit a decomposition with respect to primal and dual variables by two-level algorithms instead of three-level algorithms. Audience: This book is addressed to specialists in operations research, optimization, and optimal control Mathematics Systems theory Mathematical optimization Optimization Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematical Modeling and Industrial Mathematics Mathematik Dekomposition (DE-588)4149030-7 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s Dekomposition (DE-588)4149030-7 s 1\p DE-604 https://doi.org/10.1007/978-1-4757-3243-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tsurkov, Vladimir Large-scale Optimization — Problems and Methods Mathematics Systems theory Mathematical optimization Optimization Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematical Modeling and Industrial Mathematics Mathematik Dekomposition (DE-588)4149030-7 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4149030-7 (DE-588)4043664-0 |
| title | Large-scale Optimization — Problems and Methods |
| title_auth | Large-scale Optimization — Problems and Methods |
| title_exact_search | Large-scale Optimization — Problems and Methods |
| title_full | Large-scale Optimization — Problems and Methods by Vladimir Tsurkov |
| title_fullStr | Large-scale Optimization — Problems and Methods by Vladimir Tsurkov |
| title_full_unstemmed | Large-scale Optimization — Problems and Methods by Vladimir Tsurkov |
| title_short | Large-scale Optimization — Problems and Methods |
| title_sort | large scale optimization problems and methods |
| topic | Mathematics Systems theory Mathematical optimization Optimization Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematical Modeling and Industrial Mathematics Mathematik Dekomposition (DE-588)4149030-7 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Mathematics Systems theory Mathematical optimization Optimization Calculus of Variations and Optimal Control; Optimization Systems Theory, Control Mathematical Modeling and Industrial Mathematics Mathematik Dekomposition Optimierung |
| url | https://doi.org/10.1007/978-1-4757-3243-6 |
| work_keys_str_mv | AT tsurkovvladimir largescaleoptimizationproblemsandmethods |