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 17:14, 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.