Optimization Tips and Tricks

Tips and tricks for use of the optimization toolbox, linear and nonlinear regression.

New users and old of optimization in MATLAB will find useful tips and tricks in this document, as well as examples one can use as templates for their own problems.
Use this tool by editing the file optimtips.m, then execute blocks of code in cell mode from the editor, or best, publish the file to HTML. Copy and paste also works of course.

Some readers may find this tool valuable if only for the function pleas - a partitioned least squares solver based on lsqnonlin.

This is a work in progress, as I fully expect to add new topics as I think of them or as suggestions are made. Suggestions for topics I've missed are welcome, as are corrections of my probable numerous errors. The topics currently covered are listed below.

Contents
1. Linear regression basics in matlab
2. Polynomial regression models
3. Weighted regression models
4. Robust estimation
5. Ridge regression
6. Transforming a nonlinear problem to linearity
7. Sums of exponentials
8. Poor starting values
9. Before you have a problem
10. Tolerances & stopping criteria
11. Common optimization problems & mistakes
12. Partitioned least squares estimation
13. Errors in variables regression
14. Passing extra information/variables into an optimization
15. Minimizing the sum of absolute deviations
16. Minimize the maximum absolute deviation
17. Batching small problems into large problems
18. Global solutions & domains of attraction
19. Bound constrained problems
20. Inclusive versus exclusive bound constraints
21. Mixed integer/discrete problems
22. Understanding how they work
23. Wrapping an optimizer around quad
24. Graphical tools for understanding sets of nonlinear equations
25. Optimizing non-smooth or stochastic functions
26. Linear equality constraints
27. Sums of squares surfaces and the geometry of a regression
28. Confidence limits on a regression model
29. Confidence limits on the parameters in a nonlinear regression
30. Quadprog example, unrounding a curve
31. R^2
32. Estimation of the parameters of an implicit function
33. Robust fitting schemes
34. Homotopies
35. Orthogonal polynomial regression
36. Potential topics to be added or expanded in the (near) future