# 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