Practical methods of optimization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2007
|
| Ausgabe: | 2. ed., reprint. |
| Schriftenreihe: | A Wiley-Interscience publication
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XIV, 436 S. graph. Darst. |
| ISBN: | 9780471494638 0471494631 0471915475 |
Internformat
MARC
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| 245 | 1 | 0 | |a Practical methods of optimization |c R. Fletcher |
| 250 | |a 2. ed., reprint. | ||
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2007 | |
| 300 | |a XIV, 436 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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Datensatz im Suchindex
| _version_ | 1804137365597323264 |
|---|---|
| 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
v¡
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
.............
ПО
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
Generał
Linearly Constrained Optimization
...... 259
11.1
Equality Constraints
............... 259
11.2
Inequality Constraints
............... 264
11.3
Zigzagging
................... 268
Questions for Chapter
Π
................ 275
Chapter
12
Nonlinear Programming
............ 277
12.1
Penalty and Barrier Functions
............ 277
12.2
Multiplier Penalty Functions
............ 287
12.3
The Lx 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
Practical
Methods of Optimization
R.
Fïetcher
Department of Mathematics and Computer Science, University of Dundee, UK
This established textbook is noted for its coverage of optimization methods that are of practical
importance. It provides a thorough treatment of standard methods such as linear and quadratic
programming, Newton-like methods and the conjugate gradient method. The theoretical
aspects of the subject include an extended treatment of
optimałity
conditions and the
significance of
Lagrange
multipliers. The relevance of convexity theory to optimization is also
not neglected.
A significant proportion of the book is devoted to the solution of nonlinear problems, with an
authoritative treatment of current methodology. Thus state of the art techniques such as the
BFGS method, trust region methods and the SQP method are described and analysed. Other
features are an extensive treatment of nonsmooth optimization and the
Ц
penalty function.
Contents
Part
1
Unœnsteined
Optimizate
Part
2
Constrained Optimization
1
1ntroduction
7
Introduction
2
Structure of Methods
S
Linear Programming
3
Newton-like Methods
9
The Theory of Constrained Optimization
4
Conjugate Direction Methods
10
Quadratic Programming
5
Restricted Step Methods
11
General Linearly Constrained Optimization
6
Sums of Squares and Nonlinear Equations
12
Nonlinear Programming
18
Other Optimization Problems
About the
bMîoî
Professor Roger Fletcher completed his MA at the University of Cambridge in
1960
and his
PhD at the University of Leeds in
1963.
He was a lecturer at the University of Leeds from
1963
to 1969S then Principal Scientific Officer at
AERE
Harwell unffi
1973.
He then joined
ine
University of Dundee where he is Professor of Optimization and holds tie Baxter Chair of
Mathematics. In
1997
he was awarded the prestigious Dantzig Prize for
fundamente!
contributions to algorithms for nonlinear optimization,, awarded jointly by
Оте
Society for
industrial and Applied Mathematics and the
Mathematica!
Programming Society. He is
a Fetow
of tie Royal Society of Edinburgh and of the institute of Mathematics and
lis
Applications.
|
| 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
v¡
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
.
ПО
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
Generał
Linearly Constrained Optimization
. 259
11.1
Equality Constraints
. 259
11.2
Inequality Constraints
. 264
11.3
Zigzagging
. 268
Questions for Chapter
Π
. 275
Chapter
12
Nonlinear Programming
. 277
12.1
Penalty and Barrier Functions
. 277
12.2
Multiplier Penalty Functions
. 287
12.3
The Lx 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
Practical
Methods of Optimization
R.
Fïetcher
Department of Mathematics and Computer Science, University of Dundee, UK
This established textbook is noted for its coverage of optimization methods that are of practical
importance. It provides a thorough treatment of standard methods such as linear and quadratic
programming, Newton-like methods and the conjugate gradient method. The theoretical
aspects of the subject include an extended treatment of
optimałity
conditions and the
significance of
Lagrange
multipliers. The relevance of convexity theory to optimization is also
not neglected.
A significant proportion of the book is devoted to the solution of nonlinear problems, with an
authoritative treatment of current methodology. Thus state of the art techniques such as the
BFGS method, trust region methods and the SQP method are described and analysed. Other
features are an extensive treatment of nonsmooth optimization and the
Ц
penalty function.
Contents
Part
1
Unœnsteined
Optimizate
Part
2
Constrained Optimization
1
1ntroduction
7
Introduction
2
Structure of Methods
S
Linear Programming
3
Newton-like Methods
9
The Theory of Constrained Optimization
4
Conjugate Direction Methods
10
Quadratic Programming
5
Restricted Step Methods
11
General Linearly Constrained Optimization
6
Sums of Squares and Nonlinear Equations
12
Nonlinear Programming
18
Other Optimization Problems
About the
bMîoî
Professor Roger Fletcher completed his MA at the University of Cambridge in
1960
and his
PhD at the University of Leeds in
1963.
He was a lecturer at the University of Leeds from
1963
to 1969S then Principal Scientific Officer at
AERE
Harwell unffi
1973.
He then joined
ine
University of Dundee where he is Professor of Optimization and holds tie Baxter Chair of
Mathematics. In
1997
he was awarded the prestigious Dantzig Prize for
fundamente!
contributions to algorithms for nonlinear optimization,, awarded jointly by
Оте
Society for
industrial and Applied Mathematics and the
Mathematica!
Programming Society. He is
a Fetow
of tie Royal Society of Edinburgh and of the institute of Mathematics and
lis
Applications. |
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| id | DE-604.BV023105411 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:46:27Z |
| indexdate | 2024-07-09T21:11:08Z |
| institution | BVB |
| isbn | 9780471494638 0471494631 0471915475 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016308087 |
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| physical | XIV, 436 S. graph. Darst. |
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| spelling | Fletcher, Roger Verfasser aut Practical methods of optimization R. Fletcher 2. ed., reprint. Chichester [u.a.] Wiley 2007 XIV, 436 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication Otimização matemática larpcal Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016308087&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016308087&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Fletcher, Roger Practical methods of optimization Otimização matemática larpcal 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 | Otimização matemática larpcal Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Otimização matemática Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016308087&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016308087&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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