Geometric Presolver example
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(Difference between revisions)
(New page: Assume that the following problem is massive: <center> <math>\begin{array}{rl}\mbox{find}&x\\ \mbox{subject to}&E\,x=t\\ &x\succeq_{}\mathbf{0}\end{array}</math> </center> The problem is p...) |
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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 <math>533\times 2704</math> and compatible t vector. There exists a cardinality <math>36</math> binary solution <math>x</math>. Before attempting to find it, we have no choice but to reduce | + | This file contains a real E matrix having dimension <math>533\times 2704</math> and compatible <math>t</math> vector. There exists a cardinality <math>36</math> binary 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. |
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| + | A lower bound on the number of rows of <math>\,E\in\mathbb{R}^{533\times 2704}\,</math> retained is <math>217</math>.<br> | ||
| + | A lower bound on the number of columns retained is <math>1104</math>. | ||
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| + | The present exercise is to determine those rows and columns using any contemporary presolver. | ||
Revision as of 16:48, 11 April 2013
Assume that the following problem is massive:
The problem is presumed solvable but not computable by any contemporary means. The most logical strategy is to make the problem smaller.
This file contains a real E 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 the number of rows of retained is
.
A lower bound on the number of columns retained is .
The present exercise is to determine those rows and columns using any contemporary presolver.