bueler / popdip

POPDIP: a POsitive-variables Primal-Dual Interior Point method ... this is just for fun, not research

POPDIP: a POsitive-variables Primal-Dual Interior Point method

This algorithm, implemented in Matlab/Octave, solves the following positivity-constrained n-dimensional problem with linear equality constraints:

$$\begin{matrix} \min & f(x) \\ \text{subject to} & A x = b \\ & x \ge 0 \end{matrix}$$

This project is just for fun, and not research. That is, nothing here is an original contribution beyond well-known algorithms. Specifically, POPDIP is a special case of Algorithm 16.1 in section 16.7 of the textbook Griva, Nash, & Sofer, Linear and Nonlinear Optimization, 2nd ed., SIAM Press 2009.

running examples

Go to the directory matlab/, and start Matlab or Octave. The main algorithm is in popdip.m.

    >> help popdip

To use popdip.m effectively, you will probably need a driver program. Three such examples are small.m, linear.m, and obstacle.m:

    >> small
    >> linear
    >> obstacle

documentation

Please read the PDF documentation.

This LaTeX document can be rebuilt, using pdflatex and bibtex, by doing make in the doc/ directory.

history

The first version of this project was demonstrated in my Math 661 Optimization course in Fall 2018. (See bueler.github.io/M661F18/ and look among the Matlab/Octave codes.) The current version is an example in the Fall 2022 instance of the same course; see bueler.github.io/opt/.