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Re: [Help-glpk] numerical instability

From: Michael Hennebry
Subject: Re: [Help-glpk] numerical instability
Date: Tue, 12 Jul 2011 10:11:58 -0500 (CDT)
User-agent: Alpine 1.00 (DEB 882 2007-12-20)

On Tue, 12 Jul 2011, Meketon, Marc wrote:

I thought that the three different basis factorization methods that Andrew 
developed were meant to improve numerical stability (at the cost of speed).  
Has anyone tried these?

Using "glpsol" the options are (this comes from the glpsol --help usage 

I was writing from memory and it's been a while since I actually used GLPK.

LP basis factorization options:
  --luf             LU + Forrest-Tomlin update
                    (faster, less stable; default)
  --cbg             LU + Schur complement + Bartels-Golub update
                    (slower, more stable)
  --cgr             LU + Schur complement + Givens rotation update
                    (slower, more stable)

And using the C library the options to run these factorizations are found in 
the glp_bfcp control structure.  The below comes from the GLPK documentation.

int type (default: GLP_BF_FT)
   Basis factorization type:
   GLP_BF_FT - LU + Forrest{Tomlin update;
   GLP_BF_BG - LU + Schur complement + Bartels-Golub update;
   GLP_BF_GR - LU + Schur complement + Givens rotation update.
   In case of GLP_BF_FT the update is applied to matrix U, while in cases
   of GLP_BF_BG and GLP_BF_GR the update is applied to the Schur complement.

A rather obvious thing to do is start with the default
and switch if numerical problems come up.
I suspect that one would not have to start from scratch.
One could warm start from the last basis.

On Tue, 12 Jul 2011, Meketon, Marc wrote:
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