Nonlinear optimization in finite dimensions: Morse theory, Chebyshev approximation, transversality, flows, parametric aspects
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
2000
|
| Schriftenreihe: | Nonconvex optimization and its applications
47 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 510 S. Ill., graph. Darst. |
| ISBN: | 0792365615 |
Internformat
MARC
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| 490 | 1 | |a Nonconvex optimization and its applications |v 47 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | IMAGE 1
NONLINEAR OPTIMIZATION IN
FINITE DIMENSIONS MORSE THEORY, CHEBYSHEV APPROXIMATION, TRANS
VERSALITY, FLOWS, PARAMETRIC ASPECTS
BY
HUBERTUS TH. JONGEN
AACHEN UNIVERSITY OF TECHNOLOGY, DEPARTMENT OFMATHEMATICS, AACHEN,
GERMANY
AND
PETER JONKER AND FRANK TWILT
UNIVERSITY OFTWENTE, DEPARTMENT OF MATHEMATICAL SCIENCES, ENSCHEDE, THE
NETHERLANDS
IFKJ!
MM
KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON / LONDON
IMAGE 2
CONTENTS
PREFACE IX
1 INTRODUCTION 1
1.1 LOCAL MINIMA, CRITICAL POINTS, (MORSE-)INDEX 1
1.2 CONVEXITY 4
1.3 ASYMPTOTICAL ASPECTS 7
1.4 LOCAL MINIMA IN M. 2 , CONNECTION WITH PLANAR GRAPHS 9
1.5 ONE PARAMETER DEFORMATIONS OF FUNCTIONS 12
1.6 THE BASIC IDEA OF MORSE THEORY 14
1.7 THE (MAGIC) INFINITE DIMENSIONAL CELL 18
2 MORSE THEORY (WITHOUT CONSTRAINTS) 21
2.1 C R -MANIFOLDS 21
2.2 PARTITION OFUNITY 22
2.3 VECTORFIELDS 24
2.4 SOME CONCEPTS FROM GENERAL TOPOLOGY 28
2.5 SOME CONCEPTS FROM MATRIX THEORY 34
2.6 THE FUNCTIONS N AND P 38
2.7 MORSE THEORY (WITHOUT CONSTRAINTS) FOR FUNCTIONS OF CLASS C R , R
4 40
2.8 MORSE THEORY (WITHOUT CONSTRAMTS) FOR FUNCTIONS OF CLASS C R , 1 R
3 55
2.9 THE ATTACHING OF CELLS 65
3 MORSE THEORY (WITH CONSTRAINTS) 83
3.1 C R -MANIFOLDS WITH GENERALIZED BOUNDARY, R 1 83
3.2 CRITICAL POINTS, VECTOR FIELDS 100
3.3 LOWER LEVEL SETS AND (+) KARUSH-KUHN-TUCKER POINTS 125
V
IMAGE 3
VI CONTENTS
4 CHEBYSHEV APPROXIMATION, FOCAL POINTS 155
4.1 CHEBYSHEV APPROXIMATION: INTRODUCTION, REDUCTION THEOREM . . 155 4.2
FUNCTIONS OF MAXIMUM TYPE 162
4.3 FOCAL POINT THEORY IN E N 167
4.4 FOCAL POINT THEORY FOR CHEBYSHEV APPROXIMATION 171
4.5 CHEBYSHEV APPROXIMATION: CONSTRAINTS, LOCAL MINIMA 182
5 HOMOLOGY, MORSE RELATIONS 207
5.1 SINGULAR HOMOLOGY 207
5.2 MORSE RELATIONS 226
6 STABILITY OF OPTIMIZATION PROBLEMS 237
6.1 ON THE DEPENDENCE OF CRITICAL POINTS (VALUES) ON THE PROBLEM DATA237
6.2 STABILITY OF CRITICAL POINTS 252
6.3 STRUCTURAL STABILITY OF OPTIMIZATION PROBLEMS 259
7 TRANSVERSALITY 271
7.1 INTRODUCTION, SARD S THEOREM, REGULAER OPTIMIZATION PROBLEMS . 271
7.2 TRANSVERSAL INTERSECTION OF MANIFOLDS IN E 289
7.3 TRANSVERSALITY OF MAPPINGS 293
7.4 JET-EXTENSION, JET-TRANSVERSALITY 321
7.5 WHITNEY-REGULARITY, FINAL REMARKS 332
8 GRADIENT FIOWS 337
8.1 FLOWS, HYPERBOLIC SINGULARITIES, LINEARIZATION 337
8.2 VARIABLE METRIC AND GRADIENT SYSTEMS 354
8.3 GRADIENT SYSTEMS IN GENERAL POSITION 364
8.4 THE GRAPHS 0-1-0 AND O-N-0 376
8.5 INEQUALITY CONSTRAINTS: THE MIN-MAX DIGRAPH 383
8.6 REFLECTED GRADIENTS 388
9 NEWTON FLOWS 393
9.1 INTRODUCTION; ESSENTIAL AND EXTRANEOUS SINGULARITIES 393
9.2 SOME GLOBAL RESULTS 400
9.3 GRADIENT NEWTON FLOWS 406
9.4 MEROMORPHIC NEWTON FLOWS 427
10 PARAMETRIC ASPECTS 443
10.1 CRITICAL MANIFOLDS 443
10.2 ONE-PARAMETER FAMILIES OF FUNCTIONS (R N ) 450
10.3 ONE-PARAMETER FAMILIES OF FUNCTIONS (H ) 464
IMAGE 4
CONTENTS VII
10.4 ONE-PARAMETER FAMILIES OF CONSTRAINT SETS 472
10.5 FINAL REMARKS 490
REFERENCES 493
INDEX 505
LIST OF SYMBOLS 509
|
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| id | DE-604.BV013696550 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:50:24Z |
| institution | BVB |
| isbn | 0792365615 |
| language | English |
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| physical | X, 510 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Kluwer |
| record_format | marc |
| series | Nonconvex optimization and its applications |
| series2 | Nonconvex optimization and its applications |
| spelling | Jongen, Hubertus Th. 1947- Verfasser (DE-588)109135873 aut Nonlinear optimization in finite dimensions Morse theory, Chebyshev approximation, transversality, flows, parametric aspects by Hubertus Th. Jongen and Peter Jonker and Frank Twilt Dordrecht [u.a.] Kluwer 2000 X, 510 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nonconvex optimization and its applications 47 Mathematical optimization Morse theory 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 Nonconvex optimization and its applications 47 (DE-604)BV010085908 47 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009359706&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jongen, Hubertus Th. 1947- Jonker, Peter Twilt, Frank Nonlinear optimization in finite dimensions Morse theory, Chebyshev approximation, transversality, flows, parametric aspects Nonconvex optimization and its applications Mathematical optimization Morse theory Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4128192-5 |
| title | Nonlinear optimization in finite dimensions Morse theory, Chebyshev approximation, transversality, flows, parametric aspects |
| title_auth | Nonlinear optimization in finite dimensions Morse theory, Chebyshev approximation, transversality, flows, parametric aspects |
| title_exact_search | Nonlinear optimization in finite dimensions Morse theory, Chebyshev approximation, transversality, flows, parametric aspects |
| title_full | Nonlinear optimization in finite dimensions Morse theory, Chebyshev approximation, transversality, flows, parametric aspects by Hubertus Th. Jongen and Peter Jonker and Frank Twilt |
| title_fullStr | Nonlinear optimization in finite dimensions Morse theory, Chebyshev approximation, transversality, flows, parametric aspects by Hubertus Th. Jongen and Peter Jonker and Frank Twilt |
| title_full_unstemmed | Nonlinear optimization in finite dimensions Morse theory, Chebyshev approximation, transversality, flows, parametric aspects by Hubertus Th. Jongen and Peter Jonker and Frank Twilt |
| title_short | Nonlinear optimization in finite dimensions |
| title_sort | nonlinear optimization in finite dimensions morse theory chebyshev approximation transversality flows parametric aspects |
| title_sub | Morse theory, Chebyshev approximation, transversality, flows, parametric aspects |
| topic | Mathematical optimization Morse theory Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Mathematical optimization Morse theory Nichtlineare Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009359706&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV010085908 |
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