# User talk:Wotao.yin

### From Wikimization

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)