Attraction in numerical minimization: iteration mappings, attractors, and basins of attraction
Numerical minimization of an objective function is analyzed in this book to understand solution algorithms for optimization problems. Multiset-mappings are introduced to engineer numerical minimization as a repeated application of an iteration mapping. Ideas from numerical variational analysis are e...
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Cham]
Springer
[2018]
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| Series: | Springer briefs in optimization
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| Subjects: | |
| Summary: | Numerical minimization of an objective function is analyzed in this book to understand solution algorithms for optimization problems. Multiset-mappings are introduced to engineer numerical minimization as a repeated application of an iteration mapping. Ideas from numerical variational analysis are extended to define and explore notions of continuity and differentiability of multiset-mappings, and prove a fixed-point theorem for iteration mappings. Concepts from dynamical systems are utilized to develop notions of basin size and basin entropy. Simulations to estimate basins of attraction, to measure and classify basin size, and to compute basin are included to shed new light on convergence behavior in numerical minimization. Graduate students, researchers, and practitioners in optimization and mathematics who work theoretically to develop solution algorithms will find this book a useful resource |
| Item Description: | Includes bibliographical references |
| Physical Description: | xii, 78 Seiten Illustrationen 24 cm |
| ISBN: | 9783030040482 |
Staff View
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| id | DE-604.BV046254769 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:39:40Z |
| institution | BVB |
| isbn | 9783030040482 |
| language | English |
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| physical | xii, 78 Seiten Illustrationen 24 cm |
| publishDate | 2018 |
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| publisher | Springer |
| record_format | marc |
| series2 | Springer briefs in optimization |
| spelling | Levy, Adam Verfasser aut Attraction in numerical minimization iteration mappings, attractors, and basins of attraction Adam B. Levy [Cham] Springer [2018] © 2018 xii, 78 Seiten Illustrationen 24 cm txt rdacontent n rdamedia nc rdacarrier Springer briefs in optimization Includes bibliographical references Numerical minimization of an objective function is analyzed in this book to understand solution algorithms for optimization problems. Multiset-mappings are introduced to engineer numerical minimization as a repeated application of an iteration mapping. Ideas from numerical variational analysis are extended to define and explore notions of continuity and differentiability of multiset-mappings, and prove a fixed-point theorem for iteration mappings. Concepts from dynamical systems are utilized to develop notions of basin size and basin entropy. Simulations to estimate basins of attraction, to measure and classify basin size, and to compute basin are included to shed new light on convergence behavior in numerical minimization. Graduate students, researchers, and practitioners in optimization and mathematics who work theoretically to develop solution algorithms will find this book a useful resource Mathematical statistics / Data processing Numerical analysis Attractors (Mathematics) Erscheint auch als Online-Ausgabe 10.1007/978-3-030-04049-9 9783030040499 Erscheint auch als Online-Ausgabe Levy, Adam B. Attraction in Numerical Minimization Cham : Springer International Publishing, 2018 Online-Ressource (XII, 78 p. 49 illus. in color, online resource) 9783030040499 |
| spellingShingle | Levy, Adam Attraction in numerical minimization iteration mappings, attractors, and basins of attraction |
| title | Attraction in numerical minimization iteration mappings, attractors, and basins of attraction |
| title_auth | Attraction in numerical minimization iteration mappings, attractors, and basins of attraction |
| title_exact_search | Attraction in numerical minimization iteration mappings, attractors, and basins of attraction |
| title_full | Attraction in numerical minimization iteration mappings, attractors, and basins of attraction Adam B. Levy |
| title_fullStr | Attraction in numerical minimization iteration mappings, attractors, and basins of attraction Adam B. Levy |
| title_full_unstemmed | Attraction in numerical minimization iteration mappings, attractors, and basins of attraction Adam B. Levy |
| title_short | Attraction in numerical minimization |
| title_sort | attraction in numerical minimization iteration mappings attractors and basins of attraction |
| title_sub | iteration mappings, attractors, and basins of attraction |
| work_keys_str_mv | AT levyadam attractioninnumericalminimizationiterationmappingsattractorsandbasinsofattraction |