Iterative methods for optimization:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia, Pa.
SIAM
1999
|
| Series: | Frontiers in applied mathematics
18 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 180 S. graph. Darst. |
| ISBN: | 0898714338 9780898714333 |
Staff View
MARC
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| 100 | 1 | |a Kelley, C. T. |e Verfasser |0 (DE-588)114209642 |4 aut | |
| 245 | 1 | 0 | |a Iterative methods for optimization |c C. T. Kelley |
| 264 | 1 | |a Philadelphia, Pa. |b SIAM |c 1999 | |
| 300 | |a XV, 180 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Frontiers in applied mathematics |v 18 | |
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| 650 | 7 | |a Optimaliseren |2 gtt | |
| 650 | 7 | |a Optimisation mathématique |2 ram | |
| 650 | 7 | |a methode iterative |2 inriac | |
| 650 | 7 | |a optimisation mathematique |2 inriac | |
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Iterative methods (Mathematics) | |
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Record in the Search Index
| _version_ | 1804127406088257536 |
|---|---|
| adam_text | Contents
Preface
xiii
How to Get the Software
xv
I Optimization of Smooth Functions
1
1
Basic Concepts
3
1.1
The Problem
.................................... 3
1.2
Notation
...................................... 4
1.3
Necessary Conditions
............................... 5
1.4
Sufficient Conditions
............................... 6
1.5
Quadratic Objective Functions
.......................... 6
1.5.1
Positive Definite Hessian
......................... 7
1.5.2
Indefinite Hessian
............................. 9
1.6
Examples
..................................... 9
1.6.1
Discrete Optimal Control
......................... 9
1.6.2
Parameter Identification
......................... 11
1.6.3
Convex Quadratics
............................ 12
1.7
Exercises on Basic Concepts
........................... 12
2
Local Convergence of Newton s Method
13
2.1
Types of Convergence
............................... 13
2.2
The Standard Assumptions
............................ 14
2.3
Newton s Method
................................. 14
2.3.1
Errors in Functions, Gradients, and Hessians
.............. 17
2.3.2
Termination of the Iteration
....................... 21
2.4
Nonlinear Least Squares
............................. 22
2.4.1
Gauss-Newton Iteration
......................... 23
2.4.2
Overdetermined Problems
........................ 24
2.4.3
Underdetermined Problems
....................... 25
2.5
Inexact Newton Methods
............................. 28
2.5.1
Convergence Rates
............................ 29
2.5.2
Implementation of Newton-CG
..................... 30
2.6
Examples
..................................... 33
2.6.1
Parameter Identification
......................... 33
2.6.2
Discrete Control Problem
........................ 34
2.7
Exercises on Local Convergence
......................... 35
ix
x
CONTENTS
3 Global
Convergence
39
3.1
The Method of Steepest
Descent
......................... 39
3.2
Line Search Methods and the
Armijo
Rule
.................... 40
3.2.1
Stepsize Control with Polynomial Models
................ 43
3.2.2
Slow Convergence of Steepest Descent
................. 45
3.2.3
Damped Gauss-Newton Iteration
.................... 47
3.2.4
Nonlinear Conjugate Gradient Methods
................. 48
3.3
Trust Region Methods
............................... 50
3.3.1
Changing the Trust Region and the Step
................. 51
3.3.2
Global Convergence of Trust Region Algorithms
............ 52
3.3.3
A Unidirectional Trust Region Algorithm
................ 54
3.3.4
The Exact Solution of the Trust Region Problem
............ 55
3.3.5
The Levenberg-Marquardt Parameter
.................. 56
3.3.6 Superlinear
Convergence: The Dogleg
.................. 58
3.3.7
A Trust Region Method for Newton-CG
................. 63
3.4
Examples
..................................... 65
3.4.1
Parameter Identification
......................... 67
3.4.2
Discrete Control Problem
........................ 68
3.5
Exercises on Global Convergence
........................ 68
4
The BFGS Method
71
4.1
Analysis
...................................... 72
4.1.1
Local Theory
............................... 72
4.1.2
Global Theory
.............................. 77
4.2
Implementation
.................................. 78
4.2.1
Storage
.................................. 78
4.2.2
A BFGS-Armijo Algorithm
....................... 80
4.3
Other
Quasi-Newton
Methods
.......................... 81
4.4
Examples
..................................... 83
4.4.1
Parameter ID Problem
.......................... 83
4.4.2
Discrete Control Problem
........................ 83
4.5
Exercises on BFGS
................................ 85
5
Simple Bound Constraints
87
5.1
Problem Statement
................................ 87
5.2
Necessary Conditions for Optimality
....................... 87
5.3
Sufficient Conditions
............................... 89
5.4
The Gradient Projection Algorithm
........................ 91
5.4.1
Termination of the Iteration
....................... 91
5.4.2
Convergence Analysis
.......................... 93
5.4.3
Identification of the Active Set
...................... 95
5.4.4
A Proof of Theorem
5.2.4 ........................ 96
5.5 Superlinear
Convergence
............................. 96
5.5.1
The Scaled Gradient Projection Algorithm
................ 96
5.5.2
The Projected Newton Method
...................... 100
5.5.3
A Projected BFGS-Armijo Algorithm
.................. 102
5.6
Other Approaches
................................. 104
5.6.1
Infinite-Dimensional Problems
...................... 106
5.7
Examples
..................................... 106
5.7.1
Parameter ID Problem
.......................... 106
5.7.2
Discrete Control Problem
........................ 106
CONTENTS xi
5.8
Exercises on
Bound Constrained Optimization
.................. 108
II Optimization of Noisy Functions
109
6
Basic Concepts and Goals 111
6.1
Problem Statement
................................ 112
6.2
The Simplex Gradient
............................... 112
6.2.1
Forward Difference Simplex Gradient
.................. 113
6.2.2
Centered Difference Simplex Gradient
.................. 115
6.3
Examples
..................................... 118
6.3.1
Weber s Problem
............................. 118
6.3.2
Perturbed Convex Quadratics
...................... 119
6.3.3
Lennard-Jones Problem
......................... 120
6.4
Exercises on Basic Concepts
........................... 121
7
Implicit Filtering
123
7.1
Description and Analysis of Implicit Filtering
.................. 123
7.2
Quasi-Newton
Methods and Implicit Filtering
.................. 124
7.3
Implementation Considerations
.......................... 125
7.4
Implicit Filtering for Bound Constrained Problems
............... 126
7.5
Restarting and Minima at All Scales
....................... 127
7.6
Examples
..................................... 127
7.6.1
Weber s Problem
............................. 127
7.6.2
Parameter ID
............................... 129
7.6.3
Convex Quadratics
............................ 129
7.7
Exercises on Implicit Filtering
.......................... 133
8
Direct Search Algorithms
135
8.1
The Nelder-Mead Algorithm
........................... 135
8.1.1
Description and Implementation
..................... 135
8.1.2
Sufficient Decrease and the Simplex Gradient
.............. 137
8.1.3
MeKinnon s Examples
.......................... 139
8.1.4
Restarting the Nelder-Mead Algorithm
................. 141
8.2
Multidirectional Search
.............................. 143
8.2.1
Description and Implementation
..................... 143
8.2.2
Convergence and the Simplex Gradient
................. 144
8.3
The Hooke-Jeeves Algorithm
........................... 145
8.3.1
Description and Implementation
..................... 145
8.3.2
Convergence and the Simplex Gradient
................. 148
8.4
Other Approaches
................................. 148
8.4.1
Surrogate Models
............................. 148
8.4.2
The DIRECT Algorithm
......................... 149
8.5
Examples
..................................... 152
8.5.1
Weber s Problem
............................. 152
8.5.2
Parameter ID
............................... 153
8.5.3
Convex Quadratics
............................ 153
8.6
Exercises on Search Algorithms
......................... 159
X
CONTENTS
Bibliography
Index
|
| any_adam_object | 1 |
| author | Kelley, C. T. |
| author_GND | (DE-588)114209642 |
| author_facet | Kelley, C. T. |
| author_role | aut |
| author_sort | Kelley, C. T. |
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| building | Verbundindex |
| bvnumber | BV012738694 |
| callnumber-first | Q - Science |
| callnumber-label | QA402 |
| callnumber-raw | QA402.5.K44 1999 |
| callnumber-search | QA402.5.K44 1999 |
| callnumber-sort | QA 3402.5 K44 41999 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 870 SK 910 |
| classification_tum | MAT 912f |
| ctrlnum | (OCoLC)40734787 (DE-599)BVBBV012738694 |
| dewey-full | 519.3 519.321 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.3 519.3 21 |
| dewey-search | 519.3 519.3 21 |
| dewey-sort | 3519.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:32:50Z |
| institution | BVB |
| isbn | 0898714338 9780898714333 |
| language | English |
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| physical | XV, 180 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | SIAM |
| record_format | marc |
| series | Frontiers in applied mathematics |
| series2 | Frontiers in applied mathematics |
| spelling | Kelley, C. T. Verfasser (DE-588)114209642 aut Iterative methods for optimization C. T. Kelley Philadelphia, Pa. SIAM 1999 XV, 180 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Frontiers in applied mathematics 18 Iteratief oplossen gtt Itération (mathématiques) ram Optimaliseren gtt Optimisation mathématique ram methode iterative inriac optimisation mathematique inriac Mathematical optimization Iterative methods (Mathematics) Optimierung (DE-588)4043664-0 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Optimierung (DE-588)4043664-0 s Iteration (DE-588)4123457-1 s DE-604 Frontiers in applied mathematics 18 (DE-604)BV001873790 18 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008662095&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kelley, C. T. Iterative methods for optimization Frontiers in applied mathematics Iteratief oplossen gtt Itération (mathématiques) ram Optimaliseren gtt Optimisation mathématique ram methode iterative inriac optimisation mathematique inriac Mathematical optimization Iterative methods (Mathematics) Optimierung (DE-588)4043664-0 gnd Iteration (DE-588)4123457-1 gnd |
| subject_GND | (DE-588)4043664-0 (DE-588)4123457-1 |
| title | Iterative methods for optimization |
| title_auth | Iterative methods for optimization |
| title_exact_search | Iterative methods for optimization |
| title_full | Iterative methods for optimization C. T. Kelley |
| title_fullStr | Iterative methods for optimization C. T. Kelley |
| title_full_unstemmed | Iterative methods for optimization C. T. Kelley |
| title_short | Iterative methods for optimization |
| title_sort | iterative methods for optimization |
| topic | Iteratief oplossen gtt Itération (mathématiques) ram Optimaliseren gtt Optimisation mathématique ram methode iterative inriac optimisation mathematique inriac Mathematical optimization Iterative methods (Mathematics) Optimierung (DE-588)4043664-0 gnd Iteration (DE-588)4123457-1 gnd |
| topic_facet | Iteratief oplossen Itération (mathématiques) Optimaliseren Optimisation mathématique methode iterative optimisation mathematique Mathematical optimization Iterative methods (Mathematics) Optimierung Iteration |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008662095&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001873790 |
| work_keys_str_mv | AT kelleyct iterativemethodsforoptimization |