Nonlinear Parameter Optimization Using R Tools

Content: Cover
Title Page
Copyright
Contents
Preface
Chapter 1 Optimization problem tasks and how they arise
1.1 The general optimization problem
1.2 Why the general problem is generally uninteresting
1.3 (Non- )Linearity
1.4 Objective function properties
1.4.1 Sums of squares
1.4.2 Minimax approximation
1.4.3 Problems with multiple minima
1.4.4 Objectives that can only be imprecisely computed
1.5 Constraint types
1.6 Solving sets of equations
1.7 Conditions for optimality
1.8 Other classifications
References
Chapter 2 Optimization algorithms-an overview. 2.1 Methods that use the gradient2.2 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
2.10.1 Numerical approximation of gradients
2.10.2 Approximate and descend
2.10.3 Heuristic search
2.11 Stochastic methods
2.12 Constraint-based methods-mathematical programming
References. Chapter 3 Software structure and interfaces3.1 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
3.5.1 Use of ""global'' data and variables
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 calculations3.14 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
4.1 Roots
4.2 Equations in one variable
4.3 Some examples
4.3.1 Exponentially speaking
4.3.2 A normal concern
4.3.3 Little Polly Nomial
4.3.4 A hypothequial question
4.4 Approaches to solving 1D root-finding problems
4.5 What can go wrong?
4.6 Being a smart user of root-finding programs. 4.7 Conclusions and extensionsReferences
Chapter 5 One-parameter minimization problems
5.1 The optimize() function
5.2 Using a root-finder
5.3 But where is the minimum?
5.4 Ideas for 1D minimizers
5.5 The line-search subproblem
References
Chapter 6 Nonlinear least squares
6.1 nls() from package stats
6.1.1 A simple example
6.1.2 Regression versus least squares
6.2 A more difficult case
6.3 The structure of the nls() solution
6.4 Concerns with nls()
6.4.1 Small residuals
6.4.2 Robustness-""singular gradient'' woes
6.4.3 Bounds with nls().