# Geometric Presolver example

(Difference between revisions)
 Revision as of 16:48, 11 April 2013 (edit)← Previous diff Revision as of 16:54, 11 April 2013 (edit) (undo)Next diff → Line 8: Line 8: The most logical strategy is to make the problem smaller. The most logical strategy is to make the problem smaller. - This file contains a real E matrix having dimension $533\times 2704$ and compatible $t$ vector. There exists a cardinality $36$ binary solution $x$. Before attempting to find it, we presume to have no choice but to reduce dimension of the $E$ matrix prior to computing a solution. + [http://www.convexoptimization.com/TOOLS/EAndy.mat This Matlab workspace file] + contains a real $E$ matrix having dimension $533\times 2704$ and compatible $t$ vector. There exists a cardinality $36$ binary solution $x$. Before attempting to find it, we presume to have no choice but to reduce dimension of the $E$ matrix prior to computing a solution. A lower bound on the number of rows of $\,E\in\mathbb{R}^{533\times 2704}\,$ retained is $217$.
A lower bound on the number of rows of $\,E\in\mathbb{R}^{533\times 2704}\,$ retained is $217$.

## Revision as of 16:54, 11 April 2013

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 Matlab workspace file contains a real $LaTeX: E$ matrix having dimension $LaTeX: 533\times 2704$ and compatible $LaTeX: t$ vector. There exists a cardinality $LaTeX: 36$ 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.