User talk:Wotao.yin
From Wikimization
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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. | 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. | ||
- | 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 been discarded | + | 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) |
Revision as of 19:19, 5 November 2010
I regard the following as a very difficult problem, having spent considerable time with it.
Rectangular submatrix comes 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. It contains only 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)