Hierarchical Optimization and Mathematical Physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
2000
|
| Schriftenreihe: | Applied Optimization
37 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book should be considered as an introduction to a special dass of hierarchical systems of optimal control, where subsystems are described by partial differential equations of various types. Optimization is carried out by means of a two-level scheme, where the center optimizes coordination for the upper level and subsystems find the optimal solutions for independent local problems. The main algorithm is a method of iterative aggregation. The coordinator solves the problem with macrovariables, whose number is less than the number of initial variables. This problem is often very simple. On the lower level, we have the usual optimal control problems of mathematical physics, which are far simpler than the initial statements. Thus, the decomposition (or reduction to problems of less dimensions) is obtained. The algorithm constructs a sequence of so-called disaggregated solutions that are feasible for the main problem and converge to its optimal solution under certain assumptions ( e.g., under strict convexity of the input functions). Thus, we bridge the gap between two disciplines: optimization theory of large-scale systems and mathematical physics. The first motivation was a special model of branch planning, where the final product obeys a preset assortment relation. The ratio coefficient is maximized. Constraints are given in the form of linear inequalities with block diagonal structure of the part of a matrix that corresponds to subsystems. The central coordinator assembles the final production from the components produced by the subsystems |
| Beschreibung: | 1 Online-Ressource (X, 310 p) |
| ISBN: | 9781461546672 9781461371120 |
| ISSN: | 1384-6485 |
| DOI: | 10.1007/978-1-4615-4667-2 |
Internformat
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| 500 | |a This book should be considered as an introduction to a special dass of hierarchical systems of optimal control, where subsystems are described by partial differential equations of various types. Optimization is carried out by means of a two-level scheme, where the center optimizes coordination for the upper level and subsystems find the optimal solutions for independent local problems. The main algorithm is a method of iterative aggregation. The coordinator solves the problem with macrovariables, whose number is less than the number of initial variables. This problem is often very simple. On the lower level, we have the usual optimal control problems of mathematical physics, which are far simpler than the initial statements. Thus, the decomposition (or reduction to problems of less dimensions) is obtained. The algorithm constructs a sequence of so-called disaggregated solutions that are feasible for the main problem and converge to its optimal solution under certain assumptions ( e.g., under strict convexity of the input functions). Thus, we bridge the gap between two disciplines: optimization theory of large-scale systems and mathematical physics. The first motivation was a special model of branch planning, where the final product obeys a preset assortment relation. The ratio coefficient is maximized. Constraints are given in the form of linear inequalities with block diagonal structure of the part of a matrix that corresponds to subsystems. The central coordinator assembles the final production from the components produced by the subsystems | ||
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Datensatz im Suchindex
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| dewey-full | 519 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4615-4667-2 |
| format | Electronic eBook |
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| id | DE-604.BV042420886 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461546672 9781461371120 |
| issn | 1384-6485 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856303 |
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| physical | 1 Online-Ressource (X, 310 p) |
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| publishDate | 2000 |
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| publisher | Springer US |
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| series | Applied Optimization |
| series2 | Applied Optimization |
| spelling | Curkov, Vladimir Ivanović 20. Jht. Verfasser (DE-588)1089276834 aut Hierarchical Optimization and Mathematical Physics by Vladimir Tsurkov Boston, MA Springer US 2000 1 Online-Ressource (X, 310 p) txt rdacontent c rdamedia cr rdacarrier Applied Optimization 37 1384-6485 This book should be considered as an introduction to a special dass of hierarchical systems of optimal control, where subsystems are described by partial differential equations of various types. Optimization is carried out by means of a two-level scheme, where the center optimizes coordination for the upper level and subsystems find the optimal solutions for independent local problems. The main algorithm is a method of iterative aggregation. The coordinator solves the problem with macrovariables, whose number is less than the number of initial variables. This problem is often very simple. On the lower level, we have the usual optimal control problems of mathematical physics, which are far simpler than the initial statements. Thus, the decomposition (or reduction to problems of less dimensions) is obtained. The algorithm constructs a sequence of so-called disaggregated solutions that are feasible for the main problem and converge to its optimal solution under certain assumptions ( e.g., under strict convexity of the input functions). Thus, we bridge the gap between two disciplines: optimization theory of large-scale systems and mathematical physics. The first motivation was a special model of branch planning, where the final product obeys a preset assortment relation. The ratio coefficient is maximized. Constraints are given in the form of linear inequalities with block diagonal structure of the part of a matrix that corresponds to subsystems. The central coordinator assembles the final production from the components produced by the subsystems Mathematics Systems theory Mathematical optimization Economics Systems Theory, Control Optimization Calculus of Variations and Optimal Control; Optimization Applications of Mathematics Economic Theory Mathematik Wirtschaft Applied Optimization 37 (DE-604)BV010841718 37 https://doi.org/10.1007/978-1-4615-4667-2 Verlag Volltext |
| spellingShingle | Curkov, Vladimir Ivanović 20. Jht Hierarchical Optimization and Mathematical Physics Applied Optimization Mathematics Systems theory Mathematical optimization Economics Systems Theory, Control Optimization Calculus of Variations and Optimal Control; Optimization Applications of Mathematics Economic Theory Mathematik Wirtschaft |
| title | Hierarchical Optimization and Mathematical Physics |
| title_auth | Hierarchical Optimization and Mathematical Physics |
| title_exact_search | Hierarchical Optimization and Mathematical Physics |
| title_full | Hierarchical Optimization and Mathematical Physics by Vladimir Tsurkov |
| title_fullStr | Hierarchical Optimization and Mathematical Physics by Vladimir Tsurkov |
| title_full_unstemmed | Hierarchical Optimization and Mathematical Physics by Vladimir Tsurkov |
| title_short | Hierarchical Optimization and Mathematical Physics |
| title_sort | hierarchical optimization and mathematical physics |
| topic | Mathematics Systems theory Mathematical optimization Economics Systems Theory, Control Optimization Calculus of Variations and Optimal Control; Optimization Applications of Mathematics Economic Theory Mathematik Wirtschaft |
| topic_facet | Mathematics Systems theory Mathematical optimization Economics Systems Theory, Control Optimization Calculus of Variations and Optimal Control; Optimization Applications of Mathematics Economic Theory Mathematik Wirtschaft |
| url | https://doi.org/10.1007/978-1-4615-4667-2 |
| volume_link | (DE-604)BV010841718 |
| work_keys_str_mv | AT curkovvladimirivanovic hierarchicaloptimizationandmathematicalphysics |