[Coin-lpsolver] Using ClpCholesky??? classes for computing projections

[Mikhail Nediak]

Hi, John,

Thanks for your earlier reply. I think that it is fine for my purposes
if any ClpCholesky??? class provides a factorization of A*A^T, where A
is a submatrix of equality constraints, and can solve a square system of
equations with this factorization. It appears to me now that it does but
I would like to check if I understand the procedure correctly:

// 1. Initialize one of ClpCholesky classes, e.g.
ClpCholeskyBase chol;
// 2. Call it for my current ClpInterior* model:
chol.order(model);
// 3. Call symbolic factorization:
chol.symbolic();
// 4. Call factorization with all ones in the diagonal
// and rowsDropped indicating inequality constraints:
...
chol.factorize(diagonal, rowsDropped);
// 5. Finally, solve the system A*A^T*lambda = region
// by calling
chol.solve(region);
// The answer (lambda) is contained in region (the elements 
// of region corresponding to the complement of rowsDropped)

I was also wondering if Clp works well with TAUCS (I did not see an
obvious place to enable it in makefiles, although ClpCholeskyTaucs is
provided), and whether do you think it is better to use native Clp
factorization with AMD ordering, or TAUCS.

Thank you very much for your advice.

Best,
Mikhail

On Thu, 2005-08-11 at 12:20, John J Forrest wrote:
> Mikhail,
> 
> What you probably want is some simplification of findDirectionVector
> in ClpPredictorCorrector class.  See if you can figure out what you
> would need.
> 
> John Forrest
> 
> 
> Mikhail Nediak
> <mnediak at business.queensu.ca>
> Sent by:
> coin-lpsolver-bounces at list.coin-or.org
> 
> 08/11/2005 09:29 AM
>                To
> coin-lpsolver at list.coin-or.org
>                cc
> 
>           Subject
> [Coin-lpsolver]
> Using
> ClpCholesky???
> classes for
> computing      
> projections
> 
> 
> 
> 
> Dear COIN Community,
> 
> I am implementing a numerical procedure which already uses ClpInterior
> to solve LPs. In this procedure, I also need to frequently compute
> projections on the subspace of LP's equality constraints. While I can
> certainly use some other linear algebra packages to do that, I was
> wondering if such functionality is already provided in some convenient
> way by ClpCholesky??? classes. Unfortunately, I was not able to
> immediately figure that out by looking at the source.
> 
> Thanks for any advice.
> 
> Best,
> Mikhail Nediak
> 
> 
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