Re: [Help-glpk] [Fwd: Initial Basis Matrix is Singular]

[Andrew Makhorin]

> I didn't see either function mentioned in the reference manual; if it
> is there, then what page is it on?

For glpk v4.45 see Section 2.6 "LP Basis Constructing Routines", pp.
45-47. The reference manual (file glpk.pdf) is included in the glpk
distribution tarball and can be found in subdirectory doc.

GLPK distribution can be ftp'ed from <ftp://ftp.gnu.org/gnu/glpk/> or
from some mirror ftp sites; see <http://www.gnu.org/order/ftp.html>.

> 
> I did find some documentation in the source code.  According to my
> understanding, the basis built by glp_std_basis contains exactly the
> auxiliary variables where the basis built by glp_adv_basis will try to
> replace *fixed* auxiliary variables with non-fixed structural variables
> that preserve the triangularity of the basis matrix.  For my
> application, each of the many LPs will contain precisely one fixed
> auxiliary variable but the LPs are generally dense so that you won't be
> able to include a structural variable while maintaining the triangular
> structure of the basis matrix.  Hence for my application, calling
> glp_adv_basis will cause the code to perform some extra work just to
> produce the same trivial initial basis that glp_std_basis.  Am I
> correct?

Yes.

>   If so, then for my application it will be more efficient to
> call glp_std_basis.
> 

Yes.