Book description
Nonlinear Parameter Optimization Using R
John C. Nash, Telfer School of Management, University of Ottawa, Canada
A systematic and comprehensive treatment of optimization software using R
In recent decades, optimization techniques have been streamlined by computational and artificial intelligence methods to analyze more variables, especially under non-linear, multivariable conditions, more quickly than ever before.
Optimization is an important tool for decision science and for the analysis of physical systems used in engineering. Nonlinear Parameter Optimization with R explores the principal tools available in R for function minimization, optimization, and nonlinear parameter determination and features numerous examples throughout.
Nonlinear Parameter Optimization with R:
Provides a comprehensive treatment of optimization techniques
Examines optimization problems that arise in statistics and how to solve them using R
Enables researchers and practitioners to solve parameter determination problems
Presents traditional methods as well as recent developments in R
Is supported by an accompanying website featuring R code, examples and datasets
Researchers and practitioners who have to solve parameter determination problems who are users of R but are novices in the field optimization or function minimization will benefit from this book. It will also be useful for scientists building and estimating nonlinear models in various fields such as hydrology, sports forecasting, ecology, chemical engineering, pharmaco-kinetics, agriculture, economics and statistics.
Table of contents
- Cover
- Title Page
- Copyright
- Dedication
- Preface
- Chapter 1: Optimization problem tasks and how they arise
-
Chapter 2: Optimization algorithms—an overview
- 2.1 Methods that use the gradient
- 2.2 Newton-like methods
- 2.3 The promise of Newton's method
- 2.4 Caution: convergence versus termination
- 2.5 Difficulties with Newton's method
- 2.6 Least squares: Gauss–Newton methods
- 2.7 Quasi-Newton or variable metric method
- 2.8 Conjugate gradient and related methods
- 2.9 Other gradient methods
- 2.10 Derivative-free methods
- 2.11 Stochastic methods
- 2.12 Constraint-based methods—mathematical programming
- References
-
Chapter 3: Software structure and interfaces
- 3.1 Perspective
- 3.2 Issues of choice
- 3.3 Software issues
- 3.4 Specifying the objective and constraints to the optimizer
- 3.5 Communicating exogenous data to problem definition functions
- 3.6 Masked (temporarily fixed) optimization parameters
- 3.7 Dealing with inadmissible results
- 3.8 Providing derivatives for functions
- 3.9 Derivative approximations when there are constraints
- 3.10 Scaling of parameters and function
- 3.11 Normal ending of computations
- 3.12 Termination tests—abnormal ending
- 3.13 Output to monitor progress of calculations
- 3.14 Output of the optimization results
- 3.15 Controls for the optimizer
- 3.16 Default control settings
- 3.17 Measuring performance
- 3.18 The optimization interface
- References
- Chapter 4: One-parameter root-finding problems
- Chapter 5: One-parameter minimization problems
-
Chapter 6: Nonlinear least squares
- 6.1 nls() from package stats
- 6.2 A more difficult case
- 6.3 The structure of the nls() solution
- 6.4 Concerns with nls()
- 6.5 Some ancillary tools for nonlinear least squares
- 6.6 Minimizing R functions that compute sums of squares
- 6.7 Choosing an approach
- 6.8 Separable sums of squares problems
- 6.9 Strategies for nonlinear least squares
- References
- Chapter 7: Nonlinear equations
- Chapter 8: Function minimization tools in the base R system
- Chapter 9: Add-in function minimization packages for R
- Chapter 10: Calculating and using derivatives
-
Chapter 11: Bounds constraints
- 11.1 Single bound: use of a logarithmic transformation
- 11.2 Interval bounds: Use of a hyperbolic transformation
- 11.3 Setting the objective large when bounds are violated
- 11.4 An active set approach
- 11.5 Checking bounds
- 11.6 The importance of using bounds intelligently
- 11.7 Post-solution information for bounded problems
- Appendix 11.A Function transfinite
- References
- Chapter 12: Using masks
- Chapter 13: Handling general constraints
- Chapter 14: Applications of mathematical programming
- Chapter 15: Global optimization and stochastic methods
-
Chapter 16: Scaling and reparameterization
- 16.1 Why scale or reparameterize?
- 16.2 Formalities of scaling and reparameterization
- 16.3 Hobbs' weed infestation example
- 16.4 The KKT conditions and scaling
- 16.5 Reparameterization of the weeds problem
- 16.6 Scale change across the parameter space
- 16.7 Robustness of methods to starting points
- 16.8 Strategies for scaling
- References
- Chapter 17: Finding the right solution
- Chapter 18: Tuning and terminating methods
- Chapter 19: Linking R to external optimization tools
- Chapter 20: Differential equation models
- Chapter 21: Miscellaneous nonlinear estimation tools for R
- Appendix A: R packages used in examples
- Index
- End User License Agreement
Product information
- Title: Nonlinear Parameter Optimization Using R Tools
- Author(s):
- Release date: May 2014
- Publisher(s): Wiley
- ISBN: 9781118569283
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