# Geometric Presolver example

### From Wikimization

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A lower bound on number of rows of <math>\,E\in\mathbb{R}^{533\times 2704}\,</math> retained is <math>217</math>.<br> | A lower bound on number of rows of <math>\,E\in\mathbb{R}^{533\times 2704}\,</math> retained is <math>217</math>.<br> | ||

- | A lower bound on number of columns retained is <math>1104</math>. | + | A lower bound on number of columns retained is <math>1104</math>.<br> |

+ | An eliminated column means it is evident that the corresponding entry in solution <math>x</math> must be <math>0</math>. | ||

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

## Revision as of 13:06, 12 April 2013

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 binary 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.