Re: [Help-glpk] non-official updated version of glpk (4.63 pre-release)

[Andrew Makhorin]

> The termination test based on a fixed tolerance value (tol_dj) currently
> used in the primal simplex is not perfect. As you understand,
> multiplying the objective coefficients by a constant changes the reduced
> costs proportionally, so if you would multiply the objective, say, by
> 0.1 (for the instance above), the termination test would be passed
> successfully. The internal objective scaling I added in 4.63 helps, but
> not in all cases. The only way to avoid this situation is to use a more
> robust termination test, for example, based on a sensitivity analysis.
> 

May also note that the numerical instability detected in the dual
simplex means that some reduced costs dj's violate their zero bounds
more than the tolerance tol_dj permits, i.e. this is caused by a similar
reason, since reducing the objective coefficients would reduce dj's
making the solution dual feasible.