Practical methods of optimization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2004
|
| Ausgabe: | 2. ed., repr. in paperback |
| Schriftenreihe: | A Wiley-Interscience publication
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIV, 436 S. Ill., graph. Darst. |
| ISBN: | 9780471494638 0471494631 0471915475 |
Internformat
MARC
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| 245 | 1 | 0 | |a Practical methods of optimization |c R. Fletcher |
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| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2004 | |
| 300 | |a XIV, 436 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804133007514140672 |
|---|---|
| adam_text | Contents
Preface........................................................... ix
Table of Notation............................................... xiii
PART 1 UNCONSTRAINED OPTIMIZATION.................................. 1
Chapter 1 Introduction............................................. 3
1.1 History and Applications.................................... 3
1.2 Mathematical Background..................................... 6
Questions for Chapter 1........................................ 11
Chapter 2 Structure of Methods.................................... 12
2.1 Conditions for Local Minima................................ 12
2.2 Ad hoc Methods............................................. 16
2.3 Useful Algorithmic Properties . ........................... 19
2.4 Quadratic Models ........................................ 24
2.5 Descent Methods and Stability.............................. 26
2.6 Algorithms for the Line Search Subproblem.................. 33
Questions for Chapter 2........................................ 40
Chapter 3 Newton-like Methods .................................... 44
3.1 Newton’s Method............................................ 44
3.2 Quasi-Newton Methods..................................... 49
3.3 Invariance, Metrics and Variational Properties............. 57
3.4 The Broyden Family......................................... 62
3.5 Numerical Experiments...................................... 68
3.6 Other Formulae........................................... 72
Questions for Chapter 3. . 74
Chapter 4 Conjugate Direction Methods ............................ 80
4.1 Conjugate Gradient Methods................................. 80
vj Contents
4.2 Direction Set Methods.................................... 87
Questions for Chapter 4...................................... 92
Chapter 5 Restricted Step Methods................................ 95
5.1 A Prototype Algorithm.................................... 95
5.2 Levenberg-Marquardt Methods.................................100
Questions for Chapter 5.........................................108
Chapter 6 Sums of Squares and Nonlinear Equations...................110
6.1 Over-determined Systems.....................................110
6.2 Well-determined Systems.....................................119
6.3 No-derivative Methods.......................................129
Questions for Chapter 6.........................................133
PART 2 CONSTRAINED OPTIMIZATION 137
Chapter 7 Introduction............................................. 139
7.1 Preview.................................................... 139
7.2 Elimination and Other Transformations.......................144
Questions for Chapter 7........................................ 149
Chapter 8 Linear Programming....................................... 150
8.1 Structure.................................................. 150
8.2 The Simplex Method......................................... 153
8.3 Other LP Techniques........................................ 159
8.4 Feasible Points for Linear Constraints..................... 162
8.5 Stable and Large-scale Linear Programming................168
8.6 Degeneracy................................................. 177
8.7 Polynomial Time Algorithms................................. 183
Questions for Chapter 8........................................ 188
Chapter 9 The Theory of Constrained Optimization ....... 195
9.1 Lagrange Multipliers....................................... 195
9.2 First Order Conditions .....................................201
9.3 Second Order Conditions.....................................207
9.4 Convexity...................................................213
9.5 Duality.....................................................219
Questions for Chapter 9....................................... 224
Chapter 10 Quadratic Programming....................................229
10.1 Equality Constraints.......................................229
10.2 Lagrangian Methods.........................................236
10.3 Active Set Methods.........................................240
10.4 Advanced Features..........................................245
Contents
vu
10.5 Special QP Problems........................................247
10.6 Complementary Pivoting and Other Methods...................250
Questions for Chapter 10........................................255
Chapter 11 General Linearly Constrained Optimization..............259
11.1 Equality Constraints.......................................259
11.2 Inequality Constraints.....................................264
11.3 Zigzagging.................................................268
Questions for Chapter 11........................................275
Chapter 12 Nonlinear Programming..................................277
12.1 Penalty and Barrier Functions..............................277
12.2 Multiplier Penalty Functions...............................287
12.3 The L1 Exact Penalty Function..............................296
12.4 The Lagrange-Newton Method (SQP)...........................304
12.5 Nonlinear Elimination and Feasible Direction Methods . . . 317
12.6 Other Methods .............................................322
Questions for Chapter 12........................................325
Chapter 13 Other Optimization Problems............................331
13.1 Integer Programming........................................331
13.2 Geometric Programming......................................339
13.3 Network Programming................................... . 344
Questions for Chapter 13........................................354
Chapter 14 Non-Smooth Optimization................................357
14.1 Introduction............................................. 357
14.2 Optimality Conditions..................................... 364
14.3 Exact Penalty Functions....................................378
14.4 Algorithms.................................................382
14.5 A Globally Convergent Prototype Algorithm..................397
14.6 Constrained Non-Smooth Optimization........................402
Questions for Chapter 14. . ..................................414
References * . . . .......................................... 417
Subject Index
430
|
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| discipline | Mathematik |
| edition | 2. ed., repr. in paperback |
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| id | DE-604.BV019637153 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:01:52Z |
| institution | BVB |
| isbn | 9780471494638 0471494631 0471915475 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012966115 |
| oclc_num | 630536436 |
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| physical | XIV, 436 S. Ill., graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley-Interscience publication |
| spelling | Fletcher, Roger Verfasser aut Practical methods of optimization R. Fletcher 2. ed., repr. in paperback Chichester [u.a.] Wiley 2004 XIV, 436 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication Hier auch später erschienene, unveränderte Nachdrucke Optimización matemática (Informática) Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s DE-604 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012966115&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fletcher, Roger Practical methods of optimization Optimización matemática (Informática) Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4043664-0 |
| title | Practical methods of optimization |
| title_auth | Practical methods of optimization |
| title_exact_search | Practical methods of optimization |
| title_full | Practical methods of optimization R. Fletcher |
| title_fullStr | Practical methods of optimization R. Fletcher |
| title_full_unstemmed | Practical methods of optimization R. Fletcher |
| title_short | Practical methods of optimization |
| title_sort | practical methods of optimization |
| topic | Optimización matemática (Informática) Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Optimización matemática (Informática) Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012966115&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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