User talk:Wotao.yin
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- | + | Nonnegative rectangular submatrix <math>\,X\!\in\mathbb{R}^{1024\times256}\,</math> comes directly from a permutation matrix <math>\,\Xi\!\in\!\mathbb{R}^{1024\times1024}\,</math> having three out of every four consecutive columns discarded. This discard occurs because of structural redundancy in <math>\Xi\,</math>. | |
- | Notation <math>\mbox{vec}\,X</math> denotes vectorization; it means the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom. | + | Notation <math>\mbox{vec}\,X\!\in\mathbb{R}^{262144}</math> denotes vectorization; it means, the columns of <math>\,X</math> are stacked with column 1 on top and column 256 on the bottom. |
Matrix <math>A\!\in\!\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros. | Matrix <math>A\!\in\!\mathbb{R}^{10565\times262144}</math> is sparse having only 979,444 nonzeros. | ||
- | + | All its entries are integers from the set <math>\{{-1},0,1,2\}\,</math>. | |
+ | The 2 appears only in the fifth row from the bottom of <math>A\,</math>. | ||
Vector <math>b\,</math> is quite sparse having only a single nonzero entry: <math>1\,</math>. | Vector <math>b\,</math> is quite sparse having only a single nonzero entry: <math>1\,</math>. | ||
- | A Matlab binary | + | A [http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat Matlab binary] contains matrices <math>\,A</math> and <math>\,b</math>. |
- | + | Vector <math>c\,</math> is left unspecified because I want to vary it later as part of a | |
- | Vector <math>c\,</math> is left unspecified | + | [[Convex Iteration]]. |
- | + | Vector <math>c\,</math> may arbitrarily be set to <math>\mathbf{0}</math> or <math>\mathbf{1}</math>, for your purposes, but leave a hook for it in case you require another value. | |
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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 numerical solution begins. The [http://www.convexoptimization.com/TOOLS/Wotao.Yin/WotaoX.mat Matlab binary] possesses all 262,144 columns of <math>A\,</math>; none of its columns have yet been discarded by a presolve. | ||
--[[User:Dattorro|Dattorro]] 03:31, 5 November 2010 (PDT) | --[[User:Dattorro|Dattorro]] 03:31, 5 November 2010 (PDT) |
Current revision
I regard the following as a very difficult problem, having spent considerable time with it.
Nonnegative rectangular submatrix comes directly from a permutation matrix having three out of every four consecutive columns discarded. This discard occurs because of structural redundancy in .
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. All its entries are integers from the set . The 2 appears only in the fifth row from the bottom of .
Vector is quite sparse having only a single nonzero entry: .
A Matlab binary contains matrices and . Vector is left unspecified because I want to vary it later as part of a Convex Iteration. Vector may arbitrarily be set to or , for your purposes, but leave a hook for it in case you require another value.
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 numerical solution begins. The Matlab binary possesses all 262,144 columns of ; none of its columns have yet been discarded by a presolve.
--Dattorro 03:31, 5 November 2010 (PDT)