# Geometric Presolver example

Assume that the following problem is massive:

$LaTeX: \begin{array}{rl}\mbox{find}&x\\ \mbox{subject to}&E\,x=t\\ &x\succeq_{}\mathbf{0}\end{array}$

The problem is presumed solvable but not computable by any contemporary means. The most logical strategy is to make the problem smaller.

This file contains a real E matrix having dimension $LaTeX: 533\times 2704$ and compatible $LaTeX: t$ vector. There exists a cardinality $LaTeX: 36$ binary solution $LaTeX: x$. Before attempting to find it, we presume to have no choice but to reduce dimension of the $LaTeX: E$ matrix prior to computing a solution.

A lower bound on the number of rows of $LaTeX: \,E\in\mathbb{R}^{533\times 2704}\,$ retained is $LaTeX: 217$.
A lower bound on the number of columns retained is $LaTeX: 1104$.

The present exercise is to determine those rows and columns using any contemporary presolver.