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 nonlinear, 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, pharmacokinetics, 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 Newtonlike 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 QuasiNewton or variable metric method
 2.8 Conjugate gradient and related methods
 2.9 Other gradient methods
 2.10 Derivativefree methods
 2.11 Stochastic methods
 2.12 Constraintbased 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: Oneparameter rootfinding problems
 Chapter 5: Oneparameter 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: Addin 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 Postsolution 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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