Re: [Help-glpk] numerical instability

[Michael Hennebry]

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 
> statement):

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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Michael   address@hidden
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