[Help-glpk] verified bound on the objective value

[Ali Baharev]

Dear List Members,

We often see posts from confused users who cannot understand why GLPK
behaves weirdly for some LP instances. The suspected reason is usually
excessive round-off error. I also had a long discussion on this topic
in January:

http://lists.gnu.org/archive/html/help-glpk/2008-01/msg00029.html

Since then, i released a source code in March for computing verified
bounds on the objective value with directed rounding, for continuous
LP problems with double-bounded variables.
I released the revised code (still very rough!) on my homepage just now:

http://reliablecomputing.eu/software.html#rigorous_error_bounds

This could be an alternative to exact arithmetic. Checking the results
with directed rounding is much faster than exact arithmetic but has
its own drawbacks also.

It would be really good to extend my code, and check every node of the
search tree with directed rounding in case of MILP, unfortunately i
lack the time. If done, however, one could get the solution of the
MILP with mathematical certainty.

Suggests and help are welcome. If you have any questions concerning my
code, do not hesitate to contact me.

Best regards,

Ali