Nonlinear parameter optimization using R tools:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester
Wiley
2014
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVI, 287 S. |
| ISBN: | 9781118569283 |
Staff View
MARC
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| 010 | |a 013051141 | ||
| 020 | |a 9781118569283 |9 978-1-118-56928-3 | ||
| 035 | |a (OCoLC)891591139 | ||
| 035 | |a (DE-599)BVBBV042152674 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
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| 084 | |a QH 500 |0 (DE-625)141607: |2 rvk | ||
| 100 | 1 | |a Nash, John C. |d 1947- |e Verfasser |0 (DE-588)1045402818 |4 aut | |
| 245 | 1 | 0 | |a Nonlinear parameter optimization using R tools |c John C. Nash |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Chichester |b Wiley |c 2014 | |
| 300 | |a XVI, 287 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Mathematical optimization | |
| 650 | 4 | |a Nonlinear theories | |
| 650 | 4 | |a R (Computer program language) | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027592473&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027592473 | ||
Record in the Search Index
| _version_ | 1804152645508661248 |
|---|---|
| adam_text | Contents
Preface
xv
1
Optimization problem tasks and how they arise
1
1.1
The general optimization problem
1
1.2
Why the general problem is generally uninteresting
2
1.3
(Non-)Linearity
4
1.4
Objective function properties
4
1.4.1
Sums of squares
4
1.4.2
Minimax approximation
5
1.4.3
Problems with multiple minima
5
1.4.4
Objectives that can only be imprecisely computed
5
1.5
Constraint types
5
1.6
Solving sets of equations
6
1.7
Conditions for optimality
7
1.8
Other classifications
7
References
8
2
Optimization algorithms
-
an overview
9
2.1
Methods that use the gradient
9
2.2
Newton-like methods
12
2.3
The promise of Newton s method
13
2.4
Caution: convergence versus termination
14
2.5
Difficulties with Newton s method
14
2.6
Least squares: Gauss-Newton methods
15
2.7
Quasi-Newton
or variable metric method
17
2.8
Conjugate gradient and related methods
18
2.9
Other gradient methods
19
2.10
Derivative-free methods
19
2.10.1
Numerical approximation of gradients
19
2.10.2
Approximate and descend
19
2.10.3
Heuristic search
20
2.11
Stochastic methods
20
2.12
Constraint-based methods
-
mathematical programming
21
References
22
Software
structure
and interfaces
25
3.1
Perspective
25
3.2
Issues of choice
26
3.3
Software issues
27
3.4
Specifying the objective and constraints to the optimizer
28
3.5
Communicating exogenous data to problem
definition functions
28
3.5.1
Use of global data and variables
31
3.6
Masked (temporarily fixed) optimization parameters
32
3.7
Dealing with inadmissible results
33
3.8
Providing derivatives for functions
34
3.9
Derivative approximations when there are constraints
36
3.10
Scaling of parameters and function
36
3.11
Normal ending of computations
36
3.12
Termination tests
-
abnormal ending
37
3.13
Output to monitor progress of calculations
3 7
3.14
Output of the optimization results
38
3.15
Controls for the optimizer
38
3.16
Default control settings
39
3.17
Measuring performance
39
3.18
The optimization interface
39
References
40
One-parameter root-finding problems
41
4.1
Roots
41
4.2
Equations in one variable
42
4.3
Some examples
42
4.3.1
Exponentially speaking
42
4.3.2
A normal concern
44
4.3.3
Little Polly Nomial
46
4.3.4
A hypothequial question
49
4.4
Approaches to solving ID root-finding problems
51
4.5
What can go wrong?
52
4.6
Being a smart user of root-finding programs
54
4.7
Conclusions and extensions
54
References
55
One-parameter minimization problems
56
5.1
The optimize
()
function
56
5.2
Using a root-finder
57
5.3
But where is the minimum?
58
5.4
Ideas for ID minimizers
59
5.5
The line-search subproblem
61
References
62
6
Nonlinear least squares
63
6.1
nls
()
from package stats
63
6.1.1
A simple example
63
6.1.2
Regression versus least squares
65
6.2
A more difficult case
65
6.3
The structure of the nls
( )
solution
72
6.4
Concerns with nls
() 73
6.4.1
Small residuals
74
6.4.2
Robustness
-
singular gradient woes
75
6.4.3
Bounds with
ni s
{) 77
6.5
Some ancillary tools for nonlinear least squares
79
6.5.1
Starting values and self-starting problems
79
6.5.2
Converting model expressions to sum-of-squares functions
80
6.5.3
Help for nonlinear regression
80
6.6
Minimizing
R
functions that compute sums of squares
81
6.7
Choosing an approach
82
6.8
Separable sums of squares problems
86
6.9
Strategies for nonlinear least squares
93
References
93
7
Nonlinear equations
95
7.1
Packages and methods for nonlinear equations
95
7.1.1
BB
96
7.1.2
nleqslv
96
7.1.3
Using nonlinear least squares
96
7.1.4
Using function minimization methods
96
7.2
A simple example to compare approaches
97
7.3
A statistical example
103
References
106
8
Function minimization tools in the base
R
system
108
8.1
optim
() 108
8.2
nlmO
110
8.3
nlminbO 111
8.4
Using the base optimization tools
112
References
114
9
Add-in function minimization packages for
R
115
9.1
Package optimx
115
9.1.1
Optimizers in optimx
116
9.1.2
Example use of optimx
() 117
9.2
Some other function minimization packages
118
9.2.1
nloptr and nloptwrap
118
9.2.2
trust and trustoptim
119
9.3
Should we
replace
optimi)
routines?
121
References
122
10
Calculating and using derivatives
123
10.1
Why and how
123
10.2
Analytic derivatives
-
by hand
124
10.3
Analytic derivatives
-
tools
125
10.4
Examples of use of
R
tools for differentiation
125
10.5
Simple numerical derivatives
127
10.6
Improved numerical derivative approximations
128
10.6.1
The Richardson extrapolation
128
10.6.2
Complex-step derivative approximations
128
10.7
Strategy and tactics for derivatives
129
References
131
11
Bounds constraints
132
11.1
Single bound: use of a logarithmic transformation
132
11.2
Interval bounds: Use of a hyperbolic transformation
133
11.2.1
Example of the tanh transformation
134
11.2.2
A fly in the ointment
134
11.3
Setting the objective large when bounds are violated
135
11.4
An active set approach
136
11.5
Checking bounds
138
11.6
The importance of using bounds intelligently
138
11.6.1
Difficulties in applying bounds constraints
139
11.7
Post-solution information for bounded problems
139
Appendix
ILA
Function
transfinite
141
References
142
12
Using masks
143
12.1
An example
143
12.2
Specifying the objective
143
12.3
Masks for nonlinear least squares
147
12.4
Other approaches to masks
148
References
148
13
Handling general constraints
149
13.1
Equality constraints
149
13.1.1
Parameter elimination
151
13.1.2
Which parameter to eliminate?
153
13.1.3
Scaling and centering?
154
13.1.4
Nonlinear programming packages
154
13.1.5
Sequential application of an increasing penalty
156
13.2 Sumseale
problems
158
13.2.1
Using a projection
162
13.3
Inequality constraints
163
13.4
A perspective on penalty function ideas
167
13.5
Assessment
167
References
168
14
Applications of mathematical programming
169
14.1
Statistical applications of math programming
169
14.2
R
packages for math programming
170
14.3
Example problem: LI regression
171
14.4
Example problem: minimax regression
177
14.5
Nonlinear quantile regression
179
14.6
Polynomial approximation
180
References
183
15
Global optimization and stochastic methods
185
15.1
Panorama of methods
185
15.2
R
packages for global and stochastic optimization
186
15.3
An example problem
187
15.3.1
Method
SANN
from
optim
() 187
15.3.2
Package GenSA
188
15.3.3
Packages DEopt
im
and RcppDE
189
15.3.4
Package smco
191
15.3.5
Package
soma
192
15.3.6
Package Rmal
s cha
ins 193
15.3.7
Package rgenoud
193
15.3.8
Package
GA
194
15.3.9
Package
g
a op
t
im 195
15.4
Multiple starting values
196
References
202
16
Scaling and reparameterization
203
16.1
Why scale or reparameterize?
203
16.2
Formalities of scaling and reparameterization
204
16.3
Hobbs weed infestation example
205
16.4
The KKT conditions and scaling
210
16.5
Reparameterization of the weeds problem
214
16.6
Scale change across the parameter space
214
16.7
Robustness of methods to starting points
215
16.7.1
Robustness of optimization techniques
218
16.7.2
Robustness of nonlinear least squares methods
220
16.8
Strategies for scaling
222
References
223
17
Finding the right
solution
224
17.1
Particular requirements
224
17.1.1
A few integer parameters
225
17.2
Starting values for iterative methods
225
17.3
KKT conditions
226
17.3.1
Unconstrained problems
226
17.3.2
Constrained problems
227
17.4
Search tests
228
References
229
18
Tuning and terminating methods
230
18.1
Timing and profiling
230
18.1.1
rbenchmark
231
18.1.2
microbenchmark
231
18.1.3
Calibrating our timings
232
18.2
Profiling
234
18.2.1
Trying possible improvements
235
18.3
More speedups of
R
computations
238
18.3.1
Byte-code compiled functions
238
18.3.2
Avoiding loops
238
18.3.3
Package upgrades
-
an example
239
18.3.4
Specializing codes
241
18.4
External language compiled functions
242
18.4.1
Building an
R
function using Fortran
244
18.4.2
Summary of Rayleigh quotient timings
246
18.5
Deciding when we are finished
247
18.5.1
Tests
f
or things gone wrong
248
References
249
19
Linking
R
to external optimization tools
250
19.1
Mechanisms to link
R
to external software
251
19.1.1
R
functions to call external
(
subprograms
251
19.1.2
File and system call methods
251
19.1.3
Thin client methods
252
19.2
Prepackaged links to external optimization tools
252
19.2.1
NEOS
252
19.2.2
Automatic Differentiation Model Builder (ADMB)
252
19.2.3
NLopt
253
19.2.4
BUGS and related tools
253
19.3
Strategy for using external tools
253
References
254
20 Differential
equation models
255
20.1
The model
255
20.2
Background
256
20.3
The likelihood function
258
20.4
A first try at minimization
258
20.5
Attempts with optimx
259
20.6
Using nonlinear least squares
260
20.7
Commentary
261
Reference
262
21
Miscellaneous nonlinear estimation tools for
R
263
21.1
Maximum likelihood
263
21.2
Generalized nonlinear models
266
21.3
Systems of equations
268
21.4
Additional nonlinear least squares tools
268
21.5
Nonnegative
least squares
270
21.6
Noisy objective functions
273
21.7
Moving forward
274
References
275
Appendix A R packages used in examples
276
Index
279
|
| any_adam_object | 1 |
| author | Nash, John C. 1947- |
| author_GND | (DE-588)1045402818 |
| author_facet | Nash, John C. 1947- |
| author_role | aut |
| author_sort | Nash, John C. 1947- |
| author_variant | j c n jc jcn |
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| bvnumber | BV042152674 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 500 |
| ctrlnum | (OCoLC)891591139 (DE-599)BVBBV042152674 |
| dewey-full | 519.60285/5133 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.60285/5133 |
| dewey-search | 519.60285/5133 |
| dewey-sort | 3519.60285 45133 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV042152674 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:14:00Z |
| institution | BVB |
| isbn | 9781118569283 |
| language | English |
| lccn | 013051141 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027592473 |
| oclc_num | 891591139 |
| open_access_boolean | |
| owner | DE-739 DE-19 DE-BY-UBM DE-945 |
| owner_facet | DE-739 DE-19 DE-BY-UBM DE-945 |
| physical | XVI, 287 S. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Wiley |
| record_format | marc |
| spelling | Nash, John C. 1947- Verfasser (DE-588)1045402818 aut Nonlinear parameter optimization using R tools John C. Nash 1. publ. Chichester Wiley 2014 XVI, 287 S. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematical optimization Nonlinear theories R (Computer program language) Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027592473&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nash, John C. 1947- Nonlinear parameter optimization using R tools Mathematical optimization Nonlinear theories R (Computer program language) |
| title | Nonlinear parameter optimization using R tools |
| title_auth | Nonlinear parameter optimization using R tools |
| title_exact_search | Nonlinear parameter optimization using R tools |
| title_full | Nonlinear parameter optimization using R tools John C. Nash |
| title_fullStr | Nonlinear parameter optimization using R tools John C. Nash |
| title_full_unstemmed | Nonlinear parameter optimization using R tools John C. Nash |
| title_short | Nonlinear parameter optimization using R tools |
| title_sort | nonlinear parameter optimization using r tools |
| topic | Mathematical optimization Nonlinear theories R (Computer program language) |
| topic_facet | Mathematical optimization Nonlinear theories R (Computer program language) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027592473&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT nashjohnc nonlinearparameteroptimizationusingrtools |