# Geometric Presolver example

### From Wikimization

Assume that the following optimization problem is massive:

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 matrix having dimension and compatible vector. There exists a cardinality solution . Before attempting to find it, we presume to have no choice but to reduce dimension of the matrix prior to computing a solution.

A lower bound on number of rows of retained is .

A lower bound on number of columns retained is .

An eliminated column means it is evident that the corresponding entry in solution must be .

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