# Geometric Presolver example

(Difference between revisions)
 Revision as of 17:14, 13 April 2013 (edit)← Previous diff Current revision (17:51, 5 May 2016) (edit) (undo) Line 1: Line 1: Assume that the following optimization problem is massive: Assume that the following optimization problem is massive:
- $\begin{array}{rl}\mbox{find}&x\in\mathbb{R}^n\\ + [itex]\begin{array}{rl}\mbox{ find}&x\in\mathbb{R}^n\\ \mbox{subject to}&E\,x=t\\ \mbox{subject to}&E\,x=t\\ &x\succeq_{}\mathbf{0}\end{array}$ &x\succeq_{}\mathbf{0}\end{array}[/itex]

## Current revision

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.