- 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
Nonlinear Parameter Optimization Using R Tools
John C. Nash
Telfer School of Management
University of Ottawa
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