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Re: [Help-glpk] Fixing Numerical Instability Problems

From: Andrew Makhorin
Subject: Re: [Help-glpk] Fixing Numerical Instability Problems
Date: Fri, 18 Mar 2011 22:43:03 +0300

> It may take a little while to get the "glp_write_prob" output because I
> don't access to the computer resources needed to re-run these examples
> (they were run by a colleague on a parallel research cluster) but I do
> have a printout the LP coefficient matrices that caused a problem.  I'm
> including a number of these instances.  Note that I'm not printing out
> the last row, the last column, nor the r.h.s. because they are the same
> for every LP of a given size.  The last column contains a -1.0 in every
> entry except the lower-right corner entry which is a zero.  The last
> constraint row contains a 1.0 in every entry except the lower-right
> corner which again is a zero.  Every constraint row except the last is
> <= 0 (in glpk form, you add an artificial variable and have the
> constraint = 0).  The last constraint is = 1.0.  All of the output was
> generated by the application program except for two lines that were
> output by glpk saying that it was unable to factorize the basis matrix
> and that basis recovery hadn't been implemented yet.  The fifth and
> seventh LPs listed below were the only two in which there wasn't two or
> more identical constraint rows.  Sorry about the mail facility word
> wrapping the longer constraint rows; there doesn't seem to be a way to
> avoid it.  If this information isn't sufficient and you really need to
> see the output from glp_write_prob, let me know and I'll get that to
> you when I can.  Thanks very much for your time.

It seems to me that the error in solution is caused by some other
reason, at least not by linearly dependent rows. Since all your
instances are of small size, I'd recommend the following: remove any
calls to glp_scale_prob, and every time you need to solve a newly
generated lp instance, call glp_std_basis and then glp_simplex with the
lp presolver disabled (don't forget to check the return code from
glp_simplex). If the error will not disappear, please post me the
instances written in cplex lp or glpk format. Thanks.

Andrew Makhorin

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