Chapter 13
Optimization and Data Fitting
Optimization connects many problems in physics, from finding stable equilibria to estimating model parameters from measurements. This chapter begins with one-dimensional searches and local methods, then explores heuristic approaches for more complex search spaces. The second part develops linear and nonlinear data fitting, with attention to residuals, uncertainty, bootstrap estimates, and model selection. Throughout, the emphasis is on choosing suitable methods and checking what a numerical result actually tells us.
In this chapter
Part 1. Optimization methods
- 13.1 Mathematical formulation of optimization problems
- 13.2 One-dimensional bracketing methods
- 13.3 Local deterministic methods
- 13.4 Numerical diagnostics and failure modes
- 13.5 Heuristic global methods
- 13.6 Genetic algorithm
Part 2. Data fitting
- 13.7 What it means to model data
- 13.8 Cost functions and goodness of fit
- 13.9 Linear models and linear regression
- 13.10 Nonlinear models and parameter estimation
- 13.11 Uncertainty, noise, and robustness
- 13.12 Bootstrap methods
- 13.13 Global optimization in data modeling
- 13.14 Model comparison and selection
- 13.15 Summary and practical guidelines
- 13.16 Computational exercises and projects
Companion resources
Codes
Practical programs for one-dimensional and multidimensional optimization, heuristic search, linear and nonlinear fitting, polynomial model comparison, and bootstrap uncertainty estimates.
View Chapter 13 codes →Exercises & Projects
Additional exercises and physics projects for exploring energy minima, comparing search methods, fitting measurements, and assessing uncertainty and model choice.
View Chapter 13 exercises & projects →Resources
Method-selection guidance, practical notes on convergence, residual analysis, uncertainty estimation, and selected references.
View Chapter 13 resources →Updates & Errata
Corrections, clarifications, and post-publication updates associated with Chapter 13.
View Chapter 13 updates & errata →