Introduction to nonlinear and global optimization:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, [u.a.]
Springer
[2010]
|
| Series: | Springer optimization and its applications
37 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | xi, 208 Seiten Illustrationen |
| ISBN: | 9780387886695 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to nonlinear and global optimization |c Eligius M. T. Hendrix ; Boglárka G.-Tóth |
| 264 | 1 | |a New York, [u.a.] |b Springer |c [2010] | |
| 264 | 4 | |c © 2010 | |
| 300 | |a xi, 208 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
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Contents
Preface
їх
1
Introduction
. 1
1.1
Optimization view on mathematical models
. 1
1.2
NLP models, black-box versus explicit expression
. 3
2
Mathematical modeling, cases
. 7
2.1
Introduction
. 7
2.2
Enclosing a set of points
. 7
2.3
Dynamic decision strategies
. 10
2.4
A black box design; a sugar centrifugal screen
. 13
2.5
Design and factorial or quadratic regression
. 15
2.6
Nonlinear optimization in economic models
. 17
2.6.1
Spatial economic-ecological model
. 18
2.6.2
Neoclassical dynamic investment model for cattle
ranching
. 19
2.6.3
Several optima in environmental economics
. 19
2.7
Parameter estimation, model calibration, nonlinear regression
. 20
2.7.1
Learning of neural nets seen as parameter estimation
. 24
2.8
Summary and discussion points
. 26
2.9
Exercises
. 27
3
NLP optimality conditions
. 31
3.1
Intuition with some examples
. 31
3.2
Derivative information
. 35
3.2.1
Derivatives
. 36
3.2.2
Directional derivative
. 36
3.2.3
Gradient
. 37
3.2.4
Second-order derivative
.
r
. 38
3.2.5
Taylor
. 40
3.3
Quadratic functions
. 41
Contents
3.4 Optimality
conditions,
no binding constraints
. 45
3.4.1
First-order conditions
. 45
3.4.2
Second-order conditions
. 46
3.5
Optimality conditions, binding constraints
. 48
3.5.1 Lagrange
multiplier method
. 49
3.5.2
Karush-Kuhn-Tucker conditions
. 52
3.6
Convexity
. 54
3.6.1
First-order conditions are sufficient
. 56
3.6.2
Local minimum point is global minimum point
. 57
3.6.3
Maximum point at the boundary of the feasible area
. 59
3.7
Summary and discussion points
. 60
3.8
Exercises
. 60
3.9
Appendix: Solvers for Examples
3.2
and
3.3 . 64
Goodness of optimization algorithms
. 67
4.1
Effectiveness and efficiency of algorithms
. 67
4.1.1
Effectiveness
. 68
4.1.2
Efficiency
. 69
4.2
Some basic algorithms and their goodness
. 70
4.2.1
Introduction
. 70
4.2.2
NLP local optimization: Bisection and Newton
. 71
4.2.3
Deterministic GO: Grid search, Piyavskii^Shubert
. 74
4.2.4
Stochastic GO:
PRS, Multistart,
Simulated Annealing
. 78
4.3
Investigating algorithms
. 84
4.3.1
Characteristics
. 85
4.3-2
Comparison of algorithms
. 87
4.4
Summary and discussion points
. 88
4.5
Exercises
. 89
Nonlinear Programming algorithms
. 91
5.1
Introduction
. 91
5.1.1
General NLP problem
. 91
5.1.2
Algorithms
. 91
5.2
Minimizing functions of one variable
. 93
5.2.1
Bracketing
. 93
5.2.2
Bisection
. 94
5.2.3
Golden Section search
. 95
5.2.4
Quadratic interpolation
. 97
5.2.5
Cubic interpolation
. 99
5.2.6
Method of Newton
. 100
5.3
Algorithms not using derivative information
. 101
5.3.1
Method of
Neider
and Mead
. 102
5.3.2
Method of Powell
. 105
5.4
Algorithms using derivative information
. 106
5.4.1
Steepest descent method
. 107
Contents
vii
5.4.2 Newton
method
.
j0g
5.4.3
Conjugate gradient method
.109
5.4.4
Quasi-Newton method
.
щ
5.4.5
Inexact line search
.
цз
5.4.6
Trust region methods
.
П5
5.5
Algorithms for nonlinear regression
.118
5.5.1
Linear regression methods
.
П8
5.5.2
Gauss-Newton and Levenberg-Marquardt
.120
5.6
Algorithms for constrained optimization
.121
5.6.1
Penalty and barrier function methods
.121
5.6.2
Gradient projection method
.125
5.6.3
Sequential quadratic programming
.130
5.7
Summary and discussion points
.131
5.8
Exercises
.132
Deterministic GO algorithms
.137
6.1
Introduction
.137
6.2
Deterministic heuristic, DIRECT
.138
6.2.1
Selection for refinement
.139
6.2.2
Choice for sampling and updating rectangles
.141
6.2.3
Algorithm and illustration
.142
6.3
Stochastic models and response surfaces
.144
6.4
Mathematical structures
.147
6.4.1
Concavity
.148
6.4.2
Difference of convex functions, d.c
.149
6.4.3
Lipschitz continuity and bounds on derivatives
.150
6.4.4
Quadratic functions
.154
6.4.5
Bilinear functions
.155
6.4.6
Multiplicative and fractional functions
.156
6.4.7
Interval arithmetic
.158
6.5
Global Optimization branch and bound
.159
6.6
Examples from nonconvex quadratic programming
.161
6.6.1
Example concave quadratic programming
.162
6.6.2
Example indefinite quadratic programming
.163
6.7
Cutting planes
.165
6.8
Summary and discussion points
.16°
6.9
Exercises
.
169
Stochastic GO algorithms
.
I71
7.1
Introduction
.1^1
7.2
Random sampling in higher dimensions
.172
7.2.1
All volume to the boundary
.172
7.2.2
Loneliness in high dimensions
.173
7.3
PRS-
and Multistart-based methods
.
I74
7.3.1
Pure Random Search as benchmark
.174
viii Contents
7.3.2
Multistart
as benchmark
.176
7.3.3
Clustering to save on local searches
.178
7.3.4
Tunneling and filled functions
.180
7.4
Ideal and real, PAS and Hit and Run
.183
7.5
Population algorithms
.187
7.5.1
Controlled Random Search and Raspberries
.188
7.5.2
Genetic algorithms
.191
7.5.3
Particle swarms
.195
7.6
Summary and discussion points
.197
7.7
Exercises
.197
References
.199
Index
.205
publishes undergraduate and graduate
tbooks, monographs and state-of-the-art expository works that focus on algorithms
for solving optimization problems and applications involving such problems.
Some of the topics include optimization, network flow problems, optimal control,
multi
-objective programming, approximation and heuristic approaches.
Eligius M.T. Hendrix
·
Boglárka
G.-Tóth
Introduction to Nonlinear and Global Optimization
This self-contained text provides a solid introduction to global and nonlinear optimization,
providing students of mathematics and interdisciplinary sciences with a strong foundation
in applied optimization techniques. The book offers a unique hands-on and critical
approach to applied optimization which includes the presentation of numerous algorithms,
examples, and illustrations, designed to improve the reader's intuition and develop the
analytical skills needed to identify optimization problems, classify the structure of a model,
and determine whether a solution fulfills optimality conditions.
Key features
oí
Introduction to Nonlinear and Global Optimization:
•
Offers insights into relevant concepts such as 'regions of attraction', 'branch-and-bound',
and 'cross-cutting' methods as well as many other useful methodologies.
•
Exhibits numerical examples and exercises developing the reader's familiarity with
the terminology and algorithms that are frequently encountered in scientific literature.
•
Presents various heuristic and stochastic optimization techniques demonstrating how
each be applied to a variety of models from biology, engineering, finance, chemistry,
and economics.
This book is intended to serve as a primary text in an advanced undergraduate or graduate
course focusing on nonlinear and global optimization and requires an understanding of
basic calculus and linear algebra. |
| any_adam_object | 1 |
| author | Hendrix, Eligius M. T. 1962- G.-Tóth, Boglárka 1977- |
| author_GND | (DE-588)141413247 (DE-588)141411341 |
| author_facet | Hendrix, Eligius M. T. 1962- G.-Tóth, Boglárka 1977- |
| author_role | aut aut |
| author_sort | Hendrix, Eligius M. T. 1962- |
| author_variant | e m t h emt emth b g t bgt |
| building | Verbundindex |
| bvnumber | BV035952051 |
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| dewey-full | 519.6 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.6 |
| dewey-search | 519.6 |
| dewey-sort | 3519.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV035952051 |
| illustrated | Illustrated |
| indexdate | 2024-11-28T09:00:26Z |
| institution | BVB |
| isbn | 9780387886695 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018809092 |
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| physical | xi, 208 Seiten Illustrationen |
| publishDate | 2010 |
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| publisher | Springer |
| record_format | marc |
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| series2 | Springer optimization and its applications |
| spelling | Hendrix, Eligius M. T. 1962- (DE-588)141413247 aut Introduction to nonlinear and global optimization Eligius M. T. Hendrix ; Boglárka G.-Tóth New York, [u.a.] Springer [2010] © 2010 xi, 208 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Springer optimization and its applications Volume 37 Algorithms Mathematical optimization Globale Optimierung (DE-588)4140067-7 gnd rswk-swf Nichtlineare Optimierung (DE-588)4128192-5 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Nichtlineare Optimierung (DE-588)4128192-5 s Globale Optimierung (DE-588)4140067-7 s 1\p DE-604 DE-604 G.-Tóth, Boglárka 1977- (DE-588)141411341 aut Erscheint auch als Online-Ausgabe 978-0-387-88670-1 Springer optimization and its applications 37 (DE-604)BV021746093 37 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018809092&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018809092&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hendrix, Eligius M. T. 1962- G.-Tóth, Boglárka 1977- Introduction to nonlinear and global optimization Springer optimization and its applications Algorithms Mathematical optimization Globale Optimierung (DE-588)4140067-7 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| subject_GND | (DE-588)4140067-7 (DE-588)4128192-5 (DE-588)4151278-9 |
| title | Introduction to nonlinear and global optimization |
| title_auth | Introduction to nonlinear and global optimization |
| title_exact_search | Introduction to nonlinear and global optimization |
| title_full | Introduction to nonlinear and global optimization Eligius M. T. Hendrix ; Boglárka G.-Tóth |
| title_fullStr | Introduction to nonlinear and global optimization Eligius M. T. Hendrix ; Boglárka G.-Tóth |
| title_full_unstemmed | Introduction to nonlinear and global optimization Eligius M. T. Hendrix ; Boglárka G.-Tóth |
| title_short | Introduction to nonlinear and global optimization |
| title_sort | introduction to nonlinear and global optimization |
| topic | Algorithms Mathematical optimization Globale Optimierung (DE-588)4140067-7 gnd Nichtlineare Optimierung (DE-588)4128192-5 gnd |
| topic_facet | Algorithms Mathematical optimization Globale Optimierung Nichtlineare Optimierung Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018809092&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=018809092&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021746093 |
| work_keys_str_mv | AT hendrixeligiusmt introductiontononlinearandglobaloptimization AT gtothboglarka introductiontononlinearandglobaloptimization |