Dynamical search: applications of dynamical systems in search and optimization ; interdisciplinary statistics
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2000
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 221 S. graph. Darst. |
| ISBN: | 0849303362 |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
Notation
1 Introduction 1
2 Consistency 5
2.1 Consistency in discrete search 6
2.2 Line search algorithms 8
2.3 Consistency in linear and convex programming 19
3 Renormalisation 35
3.1 Towards a dynamical system representation 35
3.2 Renormalisation in line search algorithms 37
3.3 Renormalisation of ellipsoid algorithms 46
3.4 Renormalisation in the steepest descent algorithm 52
3.5 Square algorithm 53
4 Rates of convergence 59
4.1 Ergodic rates of convergence 59
4.2 Characteristics of average performances 61
4.3 Characteristics of worst case performances 64
4.4 Counting characteristic 64
4.5 One dimensional piecewise linear mappings 64
5 Line search algorithms 75
5.1 First order line search 75
5.2 Continued fraction expansion and the Gauss map 83
5.3 Golden Section algorithm 90
5.4 Ergodically optimal second order line search algo¬
rithm 97
CONTENTS
5.5 Symmetric algorithms 99
5.6 Midpoint and window algorithms 108
5.7 Algorithms based on section invariant numbers 113
5.8 Comparisons of GS, GS4, GS40 and window algo¬
rithms 134
5.9 The dynamic programming point of view 141
6 Ellipsoid algorithms 149
6.1 Volume optimal outer and inner ellipsoids 149
6.2 Ergodic behaviour of the outer ellipsoid algorithm
in linear programming 167
7 Steepest descent algorithm 173
7.1 Attraction to a two dimensional plane 175
7.2 Stability of attractors 182
7.3 Rate of convergence 187
7.4 Steepest descent with relaxation 188
8 Appendix 193
8.1 Entropies 193
8.2 Ergodic theory 196
8.3 Section invariant numbers 203
References 211
Author index 217
Subject index 219
|
| any_adam_object | 1 |
| author | Pronzato, Luc Wynn, Henry P. 1945- Žigljavskij, Anatolij A. |
| author_GND | (DE-588)139664033 |
| author_facet | Pronzato, Luc Wynn, Henry P. 1945- Žigljavskij, Anatolij A. |
| author_role | aut aut aut |
| author_sort | Pronzato, Luc |
| author_variant | l p lp h p w hp hpw a a ž aa aaž |
| building | Verbundindex |
| bvnumber | BV012823159 |
| classification_rvk | SK 810 SK 880 |
| ctrlnum | (OCoLC)264690859 (DE-599)BVBBV012823159 |
| dewey-full | 003 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003 |
| dewey-search | 003 |
| dewey-sort | 13 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV012823159 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:34:19Z |
| institution | BVB |
| isbn | 0849303362 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008723550 |
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| physical | 221 S. graph. Darst. |
| publishDate | 2000 |
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| publisher | Chapman & Hall/CRC |
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| spelling | Pronzato, Luc Verfasser aut Dynamical search applications of dynamical systems in search and optimization ; interdisciplinary statistics Luc Pronzato ; Henry P. Wynn ; Anatoly A. Zhigljavsky Boca Raton [u.a.] Chapman & Hall/CRC 2000 221 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differentiable dynamical systems Search theory Optimierung (DE-588)4043664-0 gnd rswk-swf Suchverfahren (DE-588)4132315-4 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Suchverfahren (DE-588)4132315-4 s Dynamisches System (DE-588)4013396-5 s DE-604 Optimierung (DE-588)4043664-0 s Wynn, Henry P. 1945- Verfasser (DE-588)139664033 aut Žigljavskij, Anatolij A. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008723550&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pronzato, Luc Wynn, Henry P. 1945- Žigljavskij, Anatolij A. Dynamical search applications of dynamical systems in search and optimization ; interdisciplinary statistics Differentiable dynamical systems Search theory Optimierung (DE-588)4043664-0 gnd Suchverfahren (DE-588)4132315-4 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4132315-4 (DE-588)4013396-5 |
| title | Dynamical search applications of dynamical systems in search and optimization ; interdisciplinary statistics |
| title_auth | Dynamical search applications of dynamical systems in search and optimization ; interdisciplinary statistics |
| title_exact_search | Dynamical search applications of dynamical systems in search and optimization ; interdisciplinary statistics |
| title_full | Dynamical search applications of dynamical systems in search and optimization ; interdisciplinary statistics Luc Pronzato ; Henry P. Wynn ; Anatoly A. Zhigljavsky |
| title_fullStr | Dynamical search applications of dynamical systems in search and optimization ; interdisciplinary statistics Luc Pronzato ; Henry P. Wynn ; Anatoly A. Zhigljavsky |
| title_full_unstemmed | Dynamical search applications of dynamical systems in search and optimization ; interdisciplinary statistics Luc Pronzato ; Henry P. Wynn ; Anatoly A. Zhigljavsky |
| title_short | Dynamical search |
| title_sort | dynamical search applications of dynamical systems in search and optimization interdisciplinary statistics |
| title_sub | applications of dynamical systems in search and optimization ; interdisciplinary statistics |
| topic | Differentiable dynamical systems Search theory Optimierung (DE-588)4043664-0 gnd Suchverfahren (DE-588)4132315-4 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Differentiable dynamical systems Search theory Optimierung Suchverfahren Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008723550&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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