Practical methods of optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2008
|
| Edition: | 2. ed., repr. in paperback |
| Series: | A Wiley-Interscience publication
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 436 Seiten Diagramme |
| ISBN: | 9780471494638 9780471915478 |
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MARC
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Record in the Search Index
| _version_ | 1804138005081882624 |
|---|---|
| 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
Chapters 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
LŁ
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
|
| adam_txt |
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
Chapters 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
LŁ
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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Fletcher, Roger 1939- |
| author_GND | (DE-588)1014948738 |
| author_facet | Fletcher, Roger 1939- |
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| author_variant | r f rf |
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| classification_rvk | QH 420 SK 870 |
| classification_tum | MAT 910f |
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| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed., repr. in paperback |
| format | Book |
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| id | DE-604.BV035060882 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:00:31Z |
| indexdate | 2024-07-09T21:21:18Z |
| institution | BVB |
| isbn | 9780471494638 9780471915478 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016729391 |
| oclc_num | 315914384 |
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| physical | XIV, 436 Seiten Diagramme |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Wiley |
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| series2 | A Wiley-Interscience publication |
| spelling | Fletcher, Roger 1939- Verfasser (DE-588)1014948738 aut Practical methods of optimization R. Fletcher 2. ed., repr. in paperback Chichester [u.a.] Wiley 2008 XIV, 436 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s DE-604 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016729391&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fletcher, Roger 1939- Practical methods of optimization 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_exact_search_txtP | 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 | Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016729391&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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