Welcome to Optimization and solving packages project!

OPTIMIZER contains experimental and development versions of R optimization packages, esp. unconstrained or box constrained problems and utilities for testing of functions, evaluating proposed solutions, and improved optimization interfaces.

The project summary page you can find here.

Packages for optimization and solution of nonlinear systems of equations could include

- large scale function minimization (sometimes in R called optimization) with box constraints
- exterior point method for general constraint optimization
- sequential quadratic programming with box constraints
- conjugate gradient minimization with box constraints
- fixed point methods
- a Levenberg-Marquardt approach to nonlinear least squares
- large scale equation solving via Barzilai-Borwein Spectral Methods for solving nonlinear system of equations
- multi-objective optimization for Nash equilibrium

Packages for utils functions include

- KKT condition testing
- numerical derivative routine
- a common interface for optimization methods

Extra documentation

Timing experiments with R based on the problem of minimizing the Rayleigh Quotient are discussed in RQtimes.Rnw, with the output file uploaded as RQtimes.pdf

Various approaches to optimization problems where parameters are constrained to obey some form of summation to a constant are described in sumscale16.Rnw, with the output file uploaded as sumscale16.pdf

There was an attempt circa 2012 to build an evolving "handbook" or "cheatsheet" for nonlinear least squares computations for R, but this seems not to have gained traction. The source file is of type .Rnw and can be processed with the knitR tools. This is nlshb.Rnw, with the latest output file uploaded as nlshb.pdf

In 2020, Hans Werner Borchers and John Nash developed a short cheatsheet for optimization tools in Base R. The source and pdf of this are BaseRCheatSheet4a.tex and BaseRCheatSheet4a.pdf

Original archival documentaion for the GPArotation package is here.