Verfügbarkeit: Nonlinear optimization in finite dimensions

Nonlinear optimization in finite dimensions: Morse theory, Chebyshev approximation, transversality, flows, parametric aspects

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Bibliographische Detailangaben
Beteiligte Personen:	Jongen, Hubertus Th. 1947- (VerfasserIn), Jonker, Peter (VerfasserIn), Twilt, Frank (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Dordrecht [u.a.] Kluwer 2000
Schriftenreihe:	Nonconvex optimization and its applications 47
Schlagwörter:	Mathematical optimization Morse theory Nichtlineare Optimierung
Links:	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
Umfang:	X, 510 S. Ill., graph. Darst.
ISBN:	0792365615

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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	2024-12-20T10:52:00Z
institution	BVB
isbn	0792365615
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-009359706
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physical	X, 510 S. Ill., graph. Darst.
publishDate	2000
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publisher	Kluwer
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series	Nonconvex optimization and its applications
series2	Nonconvex optimization and its applications
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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