Geometric Presolver example

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Assume that the following optimization problem is massive:
Assume that the following optimization problem is massive:
<center>
<center>
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<math>\begin{array}{rl}\mbox{find}&x\in\mathbb{R}^n\\
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<math>\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}</math>
&x\succeq_{}\mathbf{0}\end{array}</math>

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.

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