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Re: [Help-glpk] Almost infeasible solution, not sure what to do next

From: Andrew Makhorin
Subject: Re: [Help-glpk] Almost infeasible solution, not sure what to do next
Date: Sat, 10 Oct 2009 10:46:16 +0400

> I've a problem that is almost infeasible, its a large one, but the KKT
> conditions that glpsol gives me is:

> "KKT.PE: max.abs.err = 1.48e-12 on row 1
>         max.rel.err = 1.17e-16 on row 10
>         High quality

> KKT.PB: max.abs.err = 6.01e-07 on column 1052
>         max.rel.err = 6.01e-07 on column 1052
>         Medium quality

> KKT.DE: max.abs.err = 2.84e-14 on column 80
>         max.rel.err = 1.09e-16 on column 1168
>         High quality

> KKT.DB: max.abs.err = 0.00e+00 on row 0
>         max.rel.err = 0.00e+00 on row 0
>         High quality"

> The column that KKT.PB refers to is described thus:

> 1052 R_lipid      B    -6.0112e-07             0          1000

> My glpk code fixes this column, using GLP_FX, to have the lower and
> upper bounds of 0 and 1000, as you can see, but I don't understand why
> the output tells me that it is trying to go below zero.  I tried to
> change tolbnd so that it would allow this, but it doesn't change the
> result.  Can anyone help me by pointing out to me what the next thing
> I should try and do?

Nothing, because you have obtained the optimal basic solution. Since
your instance is degenerate, some basic variables are close to their
bounds, and some of them may slightly (within a working precision)
violate the bounds due to round-off errors. This is normal.

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