User talk:Wotao.yin
From Wikimization
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&X\geq_{}\mathbf{0}\end{array}</math> | &X\geq_{}\mathbf{0}\end{array}</math> | ||
</center> | </center> | ||
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- | Vector <math>c\,</math> is left unspecified beause I may want to vary it later in a convex iteration. | ||
- | For your purposes, it may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>. | ||
Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded. | Rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded. | ||
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A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries. This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before solution begins. | A good presolver can eliminate about 50,000 columns of <math>\,A</math> because one of the constraints '''('''fifth row from the bottom of <math>\,A\,</math>''')''' has only nonnegative entries. This means that about 50,000 entries in permutation submatrix <math>X\,</math> can be set to zero before solution begins. | ||
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+ | A Matlab binary containing matrices <math>\,A</math> and <math>\,b</math> is | ||
+ | [http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat here]. | ||
+ | Vector <math>c\,</math> is left unspecified beause I may want to vary it later in a convex iteration. | ||
+ | For your purposes, it may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>. | ||
--[[User:Dattorro|Dattorro]] 03:31, 5 November 2010 (PDT) | --[[User:Dattorro|Dattorro]] 03:31, 5 November 2010 (PDT) |
Revision as of 04:07, 5 November 2010
I regard the following as a difficult problem, having spent considerable time with it.
Rectangular submatrix comes from a permutation matrix having three out of every four consecutive columns discarded.
Notation denotes vectorization; it means the columns of are stacked with column 1 on top and column 256 on the bottom.
Matrix is sparse having only 979,444 nonzeros. It contains integers from the set .
Vector is quite sparse having only a single nonzero entry: .
A good presolver can eliminate about 50,000 columns of because one of the constraints (fifth row from the bottom of ) has only nonnegative entries. This means that about 50,000 entries in permutation submatrix can be set to zero before solution begins.
A Matlab binary containing matrices and is here. Vector is left unspecified beause I may want to vary it later in a convex iteration. For your purposes, it may arbitrarily be set to or .
--Dattorro 03:31, 5 November 2010 (PDT)