# Geometric Presolver example

Assume that the following optimization problem is massive:

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

The problem is presumed solvable but not computable by any contemporary means.
The most logical strategy is to somehow make the problem smaller.
Finding a smaller but equivalent problem is called presolving.

This Matlab workspace file contains a real $LaTeX: E$ matrix having dimension $LaTeX: 533\times 2704$ and compatible $LaTeX: t$ vector. There exists a cardinality $LaTeX: 36$ 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 number of rows of $LaTeX: \,E\in\mathbb{R}^{533\times 2704}\,$ retained is $LaTeX: 217$.
A lower bound on number of columns retained is $LaTeX: 1104$.
An eliminated column means it is evident that the corresponding entry in solution $LaTeX: x$ must be $LaTeX: 0$.

The present exercise is to determine whether any contemporary presolver can meet this lower bound.