Maxima and minima with applications: practical optimization and duality
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1999
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| Schriftenreihe: | Wiley-Interscience series in discrete mathematics and optimization
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 284 S. graph. Darst. |
| ISBN: | 0471252891 |
Internformat
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Datensatz im Suchindex
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| adam_text | MAXIMA AND MINIMA WITH APPLICATIONS PRACTICAL OPTIMIZATION AND DUALITY
WILFRED KAPLAN EMERITUS PROFESSOR OF MATHEMATICS UNIVERSITY OF MICHIGAN
A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. NEW YORK *
CHICHESTER * WEINHEIM * BRISBANE * SINGAPORE * TORONTO CONTENTS PREFACE
IX 1 MAXIMA AND MINIMA IN ANALYTIC GEOMETRY 1 1.1 MAXIMA AND MINIMA;
CASE OF FUNCTIONS OF ONE VARIABLE 1 PROBLEMS 1.1-1.5 5 1.2 CONVEXITY 6
1.3 CONVEXITY AND MAXIMA AND MINIMA 9 PROBLEMS 1.6-1.16 12 1.4 PROBLEMS
IN TWO DIMENSIONS 15 PROBLEMS 1.17-1.27 23 1.5 SOME GEOMETRIE EXTREMUM
PROBLEMS 26 PROBLEMS 1.28-1.36 30 1.6 GEOMETRY OF N-DIMENSIONAL SPACE 31
1.7 CONVEX FUNCTIONS OF N VARIABLES 36 1.8 QUADRATIC FORMS 38 PROBLEMS
1.37-1.55 41 1.9 CONVEXITY AND EXTREMA, LEVEL SETS AND SUBLEVEL SETS 45
PROBLEMS 1.56-1.63 49 1.10 STABILITY 50 1.11 GLOBAL ASYMPTOTIC
STABILITY, APPLICATION TO FINDING MINIMIZER 56 PROBLEMS 1.64-1.73 58
1.12 EXTREMA OF FUNCTIONS ON UNBOUNDED CLOSED SETS 60 1.13 SHORTEST
DISTANCE FROM A LINEAR VARIETY 63 PROBLEMS 1.74-1.84 66 1.14 OTHER INNER
PRODUCTS AND NORMS IN TV 68 1.15 MORE ON MINIMUM PROBLEMS FOR QUADRATIC
FUNCTIONS 71 PROBLEMS 1.85-1.93 74 1.16 PHYSICAL APPLICATIONS 76
PROBLEMS 1.94-1.96 78 1.17 BEST APPROXIMATION BY POLYNOMIALS 79 PROBLEMS
1.97-1.105 82 REFERENCES 83 CONTENTS 2 SIDE CONDITIONS 85 2.1 REVIEW OF
VECTOR CALCULUS 85 PROBLEMS 2.1-2.13 92 2.2 LOCAL MAXIMA AND MINIMA,
SIDE CONDITIONS 94 PROBLEMS 2.14-2.21 101 2.3 SECOND-DERIVATIVE TEST 102
PROBLEMS 2.22-2.26 105 2.4 GRADIENT METHOD FOR FINDING CRITICAL POINTS
106 PROBLEMS 2.27-2.28 108 2.5 APPLICATIONS 109 PROBLEMS 2.29-2.33 115
2.6 KARUSH-KUHN-TUCKER CONDITIONS 116 PROBLEMS 2.34-2.37 121 2.7
SUFFICIENT CONDITIONS FOR THE MATHEMATICAL PROGRAMMING PROBLEM 122 2.8
PROOF OF THE KARUSH-KUHN-TUCKER CONDITIONS 127 PROBLEMS 2.38-2.49 130
REFERENCES 134 3 OPTIMIZATION 135 3.1 CONVEXITY 135 PROBLEMS 3.1-3.17
139 3.2 MATHEMATICAL PROGRAMMING, DUALITY 142 3.3 UNCONSTRAINED
QUADRATIC OPTIMIZATION 144 PROBLEMS 3.18-3.28 146 3.4 CONSTRAINED
QUADRATIC OPTIMIZATION IN TZ 148 3.5 QP WITH INEQUALITY CONSTRAINTS, QP
ALGORITHM 153 PROBLEMS 3.29-3.38 156 3.6 LINEAR PROGRAMMING , 158 3.7
SIMPLEX ALGORITHM 166 PROBLEMS 3.39-3.55 173 3.8 LP WITH BOUNDED
VARIABLES 175 PROBLEMS 3.56-3.62 181 3.9 CONVEX FUNCTIONS AND CONVEX
PROGRAMMING 182 PROBLEMS 3.63-3.68 188 3.10 THE FERMAT-WEBER PROBLEM AND
A DUAL PROBLEM 188 PROBLEMS 3.69-3.76 193 3.11 A DUALITY RELATION IN
HIGHER DIMENSIONS 194 PROBLEMS 3.77-3.84 200 REFERENCES 201 4
FENCHEL-ROCKAFELLAR DUALITY THEORY 203 4.1 GENERALIZED DIRECTIONAL
DERIVATIVE 203 CONTENTS VII PROBLEMS 4.1-4.5 205 4.2 LOCAL STRUCTURE OF
THE BOUNDARY OF A CONVEX SET 205 PROBLEMS 4.6-4.8 209 4.3 SUPPORTING
HYPERPLANE, SEPARATING HYPERPLANE 209 PROBLEMS 4.9-4.15 216 4.4 NEW
DEFINITION OF CONVEX FUNCTION, EPIGRAPH, HYPOGRAPH 217 PROBLEMS
4.16-4.17 221 4.5 CONJUGATE OF CONVEX AND CONCAVE FUNCTIONS 221 PROBLEMS
4.18-4.24 227 4.6 FENCHEL DUALITY THEOREM 228 PROBLEMS 4.25-4.32 231 4.7
ROCKAFELLAR DUALITY THEOREM 232 4.8 PROOF OF LEMMA C 238 PROBLEMS
4.33-4.45 240 4.9 NORMS, DUAL NORMS, MINKOWSKI NORMS 242 PROBLEMS
4.46-4.61 250 4.10 GENERALIZED FERMAT-WEBER PROBLEM 252 4.11 APPLICATION
TO FACILITY LOCATION 254 PROBLEMS 4.62-4.74 259 REFERENCES 261 APPENDIX:
LINEAR ALGEBRA 263 ANSWERS TO SELECTED PROBLEMS 271 INDEX 279
|
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| id | DE-604.BV023775764 |
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| indexdate | 2024-07-09T21:36:34Z |
| institution | BVB |
| isbn | 0471252891 |
| language | English |
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| spelling | Kaplan, Wilfred 1915- Verfasser aut Maxima and minima with applications practical optimization and duality Wilfred Kaplan New York [u.a.] Wiley 1999 X, 284 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-Interscience series in discrete mathematics and optimization Análise variacional larpcal Maxima gtt Minima (natuurwetenschappen) gtt Optimaliseren gtt Programação convexa larpcal Mathematical optimization Maxima and minima Minimum (DE-588)4467521-5 gnd rswk-swf Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Maximum (DE-588)4467522-7 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Maximum (DE-588)4467522-7 s Minimum (DE-588)4467521-5 s Analytische Geometrie (DE-588)4001867-2 s Optimierung (DE-588)4043664-0 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017417982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaplan, Wilfred 1915- Maxima and minima with applications practical optimization and duality Análise variacional larpcal Maxima gtt Minima (natuurwetenschappen) gtt Optimaliseren gtt Programação convexa larpcal Mathematical optimization Maxima and minima Minimum (DE-588)4467521-5 gnd Analytische Geometrie (DE-588)4001867-2 gnd Maximum (DE-588)4467522-7 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4467521-5 (DE-588)4001867-2 (DE-588)4467522-7 (DE-588)4043664-0 |
| title | Maxima and minima with applications practical optimization and duality |
| title_auth | Maxima and minima with applications practical optimization and duality |
| title_exact_search | Maxima and minima with applications practical optimization and duality |
| title_full | Maxima and minima with applications practical optimization and duality Wilfred Kaplan |
| title_fullStr | Maxima and minima with applications practical optimization and duality Wilfred Kaplan |
| title_full_unstemmed | Maxima and minima with applications practical optimization and duality Wilfred Kaplan |
| title_short | Maxima and minima with applications |
| title_sort | maxima and minima with applications practical optimization and duality |
| title_sub | practical optimization and duality |
| topic | Análise variacional larpcal Maxima gtt Minima (natuurwetenschappen) gtt Optimaliseren gtt Programação convexa larpcal Mathematical optimization Maxima and minima Minimum (DE-588)4467521-5 gnd Analytische Geometrie (DE-588)4001867-2 gnd Maximum (DE-588)4467522-7 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Análise variacional Maxima Minima (natuurwetenschappen) Optimaliseren Programação convexa Mathematical optimization Maxima and minima Minimum Analytische Geometrie Maximum Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017417982&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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