Practical methods of optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester u.a.
Wiley
1987
|
| Edition: | 2. ed. |
| Series: | A Wiley-Interscience publication.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 417 - 429. - 1. Aufl. in 2 Bänden erschienen |
| Physical Description: | XIV, 436 S. graph. Darst. |
| ISBN: | 0471915475 |
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MARC
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| 245 | 1 | 0 | |a Practical methods of optimization |c R. Fletcher |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Chichester u.a. |b Wiley |c 1987 | |
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Record in the Search Index
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| 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
vi 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 vii
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 Lt 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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| id | DE-604.BV002133991 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:40:53Z |
| institution | BVB |
| isbn | 0471915475 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001399389 |
| oclc_num | 15429523 |
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| physical | XIV, 436 S. graph. Darst. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley-Interscience publication. |
| spelling | Fletcher, Roger Verfasser aut Practical methods of optimization R. Fletcher 2. ed. Chichester u.a. Wiley 1987 XIV, 436 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication. Literaturverz. S. 417 - 429. - 1. Aufl. in 2 Bänden erschienen Optimaliseren gtt Optimisation mathématique Wiskundige methoden gtt Mathematik Mathematical optimization Mathematics Operations Research Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001399389&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fletcher, Roger Practical methods of optimization Optimaliseren gtt Optimisation mathématique Wiskundige methoden gtt Mathematik Mathematical optimization Mathematics Operations Research 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 | Optimaliseren gtt Optimisation mathématique Wiskundige methoden gtt Mathematik Mathematical optimization Mathematics Operations Research Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Optimaliseren Optimisation mathématique Wiskundige methoden Mathematik Mathematical optimization Mathematics Operations Research Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001399389&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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