Re: [Bug-glpk] incorrect basis status

[Andrew Makhorin]

> when running GLPK 4.20 on the attached LP without presolver and
> letting it start from the standard basis (not advanced), I get a
> wrong final basis.

> The LP contains a row
> sum_{i=1..20} x_i = 1
> where the variables x_i do not appear somewhere else in the LP.
> (x_i correspond to C00000i in the mps file)

> I would expect to have at least one of the x_i in the basis,

Only if corresponding constraint is active. However, in your case
that constraint is inactive (equality constraint can be inactive if
lp is degenerative).

For example, let there be two equality constraints in an lp:

2*x1 + 2*x2 + 2*x3 = 2
3*x1 + 3*x2 + 3*x3 = 3

It is understood that at most one of them can be active; otherwise
the basis would be singular.

>  and
> that is also the case when the presolver is used or GLPK starts from
> the advanced basis (x_20 gets into the basis).

Because the lp presolver tries to remove all fixed auxiliary variables
from the basis.

>  However, when running

> glpsol --nopresol --std --mps lp03.mps -o lp03.sol

> all variables are reported as NF (see attached solution file).