# Geometric Presolver example

### From Wikimization

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[http://www.convexoptimization.com/TOOLS/EAndy.mat This Matlab workspace file] | [http://www.convexoptimization.com/TOOLS/EAndy.mat This Matlab workspace file] | ||

- | contains a real <math>E</math> matrix having dimension <math>533\times 2704</math> and compatible <math>t</math> vector. There exists a cardinality <math>36</math> | + | contains a real <math>E</math> matrix having dimension <math>533\times 2704</math> and compatible <math>t</math> vector. There exists a cardinality <math>36</math> solution <math>x</math>. Before attempting to find it, we presume to have no choice but to reduce dimension of the <math>E</math> matrix prior to computing a solution. |

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> |

## Revision as of 16:14, 13 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 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.