[Help-glpk] Fixing Numerical Instability Problems

[GLENN RHOADS]

Hi,

I have an application that solves tens of million of tiny LPs coming
from matrix games.  On checking the kkt optimality conditions, there
are a dozen cases where both the primal and dual solutions are
incorrect, and about one hundred cases with low quality dual or primal
feasibility.  The LPs were scaled using the parameter "GLP_SF_AUTO".
 I'm hoping there is some way to fix these problem cases by re-solving
the LP with different parameters.  The problem cases generally seem to
have multiple constraints that are identical; I suspect that this is
the source of the problem.

I'm thinking that I might be able to fix this by enabling the
presolver.  For efficiency reasons, it seems to make sense to
selectively enable the presolver for the LPs that don't satisfy the kkt
optimality conditions? But quoting the manual -- "Presolving may be
used when the problem instance is solved for the first time.  However,
on performing re-optimization the presolver should be disabled."  This
seems to imply that I shouldn't solve a problem with presolver disabled
and then try to correct it by re-optimizing with the presolver.  I.e. I
should use the presolver on all instances.  Is this right?  Also, since
the LPs are of the same size and are dense, I set up the LP once and
then on successive LPs, change the matrix values and reload it.  Does
this qualify as a re-optimization where the presolver should be
disabled? 

-- Glenn C. Rhoads