Asymptotic Attainability:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
383 |
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-94-017-0805-0 |
| Beschreibung: | In this monograph, questions of extensions and relaxations are considered. These questions arise in many applied problems in connection with the operation of perturbations. In some cases, the operation of "small" perturbations generates "small" deviations of basis indexes; a corresponding stability takes place. In other cases, small perturbations generate spasmodic change of a result and of solutions defining this result. These cases correspond to unstable problems. The effect of an unstability can arise in extremal problems or in other related problems. In this connection, we note the known problem of constructing the attainability domain in control theory. Of course, extremal problems and those of attainability (in abstract control theory) are connected. We exploit this connection here (see Chapter 5). However, basic attention is paid to the problem of the attainability of elements of a topological space under vanishing perturbations of restrictions. The stability property is frequently missing; the world of unstable problems is of interest for us. We construct regularizing procedures. However, in many cases, it is possible to establish a certain property similar to partial stability. We call this property asymptotic nonsensitivity or roughness under the perturbation of some restrictions. The given property means the following: in the corresponding problem, it is the same if constraints are weakened in some "directions" or not. On this basis, it is possible to construct a certain classification of constraints, selecting "directions of roughness" and "precision directions" |
| Umfang: | 1 Online-Ressource (XIV, 322 p) |
| ISBN: | 9789401708050 9789048147656 |
| DOI: | 10.1007/978-94-017-0805-0 |
Internformat
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| 500 | |a In this monograph, questions of extensions and relaxations are considered. These questions arise in many applied problems in connection with the operation of perturbations. In some cases, the operation of "small" perturbations generates "small" deviations of basis indexes; a corresponding stability takes place. In other cases, small perturbations generate spasmodic change of a result and of solutions defining this result. These cases correspond to unstable problems. The effect of an unstability can arise in extremal problems or in other related problems. In this connection, we note the known problem of constructing the attainability domain in control theory. Of course, extremal problems and those of attainability (in abstract control theory) are connected. We exploit this connection here (see Chapter 5). However, basic attention is paid to the problem of the attainability of elements of a topological space under vanishing perturbations of restrictions. The stability property is frequently missing; the world of unstable problems is of interest for us. We construct regularizing procedures. However, in many cases, it is possible to establish a certain property similar to partial stability. We call this property asymptotic nonsensitivity or roughness under the perturbation of some restrictions. The given property means the following: in the corresponding problem, it is the same if constraints are weakened in some "directions" or not. On this basis, it is possible to construct a certain classification of constraints, selecting "directions of roughness" and "precision directions" | ||
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Datensatz im Suchindex
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| id | DE-604.BV042424225 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:50Z |
| institution | BVB |
| isbn | 9789401708050 9789048147656 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859642 |
| oclc_num | 863882152 |
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| owner_facet | DE-384 DE-703 DE-91 DE-BY-TUM DE-634 |
| physical | 1 Online-Ressource (XIV, 322 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer Netherlands |
| record_format | marc |
| series | Mathematics and Its Applications |
| series2 | Mathematics and Its Applications |
| spellingShingle | Čencov, Aleksandr Georgievič 1947- Asymptotic Attainability Mathematics and Its Applications Mathematics Functional analysis Logic, Symbolic and mathematical Mathematical optimization Topology Functional Analysis Measure and Integration Calculus of Variations and Optimal Control; Optimization Mathematical Logic and Foundations Mathematik Asymptotik (DE-588)4126634-1 gnd Optimierung (DE-588)4043664-0 gnd Relaxationsmethode (DE-588)4451085-8 gnd Erreichbarkeitsmenge (DE-588)4411406-0 gnd |
| subject_GND | (DE-588)4126634-1 (DE-588)4043664-0 (DE-588)4451085-8 (DE-588)4411406-0 |
| title | Asymptotic Attainability |
| title_auth | Asymptotic Attainability |
| title_exact_search | Asymptotic Attainability |
| title_full | Asymptotic Attainability by A. G. Chentsov |
| title_fullStr | Asymptotic Attainability by A. G. Chentsov |
| title_full_unstemmed | Asymptotic Attainability by A. G. Chentsov |
| title_short | Asymptotic Attainability |
| title_sort | asymptotic attainability |
| topic | Mathematics Functional analysis Logic, Symbolic and mathematical Mathematical optimization Topology Functional Analysis Measure and Integration Calculus of Variations and Optimal Control; Optimization Mathematical Logic and Foundations Mathematik Asymptotik (DE-588)4126634-1 gnd Optimierung (DE-588)4043664-0 gnd Relaxationsmethode (DE-588)4451085-8 gnd Erreichbarkeitsmenge (DE-588)4411406-0 gnd |
| topic_facet | Mathematics Functional analysis Logic, Symbolic and mathematical Mathematical optimization Topology Functional Analysis Measure and Integration Calculus of Variations and Optimal Control; Optimization Mathematical Logic and Foundations Mathematik Asymptotik Optimierung Relaxationsmethode Erreichbarkeitsmenge |
| url | https://doi.org/10.1007/978-94-017-0805-0 |
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