Nonlinear optimization in IRn: 1 Morse theory, Chebyshev approximation
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Frankfurt am Main u.a.
Lang
1983
|
| Series: | Methoden und Verfahren der mathematischen Physik
29 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 262 S. |
| ISBN: | 3820479031 |
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| 245 | 1 | 0 | |a Nonlinear optimization in IRn |n 1 |p Morse theory, Chebyshev approximation |c H. Th. Jongen ; P. Jonker ; F. Twilt |
| 264 | 1 | |a Frankfurt am Main u.a. |b Lang |c 1983 | |
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Record in the Search Index
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| adam_text | TABLE OF CONTENTS
Preface 1
1. Introduction 3
1.1 Local minima, critical points, (morse )index 3
1.2 Convexity 6
1.3 Asymptotical aspects 9
1.4 Local minima in IT, connection with planar graphs .. 11
1.5 One parameter deformations of functions 14
1.6 The basic idea of Morse Theory 16
1.7 The (magic) infinite dimensional cell 20
2. Morse Theory (without constraints) 23
2.1 Cr manifolds 23
2.2 Partition of unity 24
2.3 Vectorfields 25
2.4 Some concepts from general topology 3O
2.5 Some concepts from matrix theory 37
2.6 The functions y and p 41
2.7 Morse Theory (without constraints)
for functions of class Cr, r 4 44
2.8 Morse Theory (without constraints)
for functions of class Cr, 1 3 3 60
2.9 The attaching of cells 71
3. Morse Theory (with constraints) 89
3.1 Cr Manifolds with Generalized Boundary, r 1 89
3.2 Critical points, vectorfields 1O8
3.3 Lower levelsets and (+) Kuhn Tucker points 135
4. Chebyshev Approximation, Focal Points 167
4.1 Chebyshev approximation: introduction, reduction
theorem 167
4.2 Functions of maximum type 175
4.3 Focal point theory in 3Rn 180
4.4 Focal point theory for Chebyshev Approximation .... 184
4.5 Chebyshev Approximation: Constraints, local
minima 197
5. Homology, Morse Relations 225
5.1 Singular homology over E 225
5.2 Morse relations 247
References 259
Index 261
Glossary of Symbols 263
|
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| id | DE-604.BV002385357 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:44:33Z |
| institution | BVB |
| isbn | 3820479031 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001552322 |
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| physical | 262 S. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Lang |
| record_format | marc |
| series | Methoden und Verfahren der mathematischen Physik |
| series2 | Methoden und Verfahren der mathematischen Physik Methoden und Verfahren der mathematischen Physik. |
| spelling | Jongen, Hubertus Th. 1947- Verfasser (DE-588)109135873 aut Nonlinear optimization in IRn 1 Morse theory, Chebyshev approximation H. Th. Jongen ; P. Jonker ; F. Twilt Frankfurt am Main u.a. Lang 1983 262 S. txt rdacontent n rdamedia nc rdacarrier Methoden und Verfahren der mathematischen Physik 29 Methoden und Verfahren der mathematischen Physik. ... Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 s DE-604 Jonker, Peter Verfasser aut Twilt, Frank Verfasser aut (DE-604)BV002385356 1 Methoden und Verfahren der mathematischen Physik 29 (DE-604)BV022072087 29 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001552322&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jongen, Hubertus Th. 1947- Jonker, Peter Twilt, Frank Nonlinear optimization in IRn Methoden und Verfahren der mathematischen Physik Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4128192-5 |
| title | Nonlinear optimization in IRn |
| title_auth | Nonlinear optimization in IRn |
| title_exact_search | Nonlinear optimization in IRn |
| title_full | Nonlinear optimization in IRn 1 Morse theory, Chebyshev approximation H. Th. Jongen ; P. Jonker ; F. Twilt |
| title_fullStr | Nonlinear optimization in IRn 1 Morse theory, Chebyshev approximation H. Th. Jongen ; P. Jonker ; F. Twilt |
| title_full_unstemmed | Nonlinear optimization in IRn 1 Morse theory, Chebyshev approximation H. Th. Jongen ; P. Jonker ; F. Twilt |
| title_short | Nonlinear optimization in IRn |
| title_sort | nonlinear optimization in irn morse theory chebyshev approximation |
| topic | Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Nichtlineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001552322&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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