Re: [Help-glpk] Numerical instability warning

[Andrew Makhorin]

> I have an application that uses glpk to solve millions of tiny LPs and
> I get several of the following messages.
> 
> Warning: numerical instability (primal simplex, phase II)
> 
> I'm not sure about the difference between a warning and an error, and
> hence, whether I need to worry about this.  I found the place in the
> code where this message is printed (in the file glpspx01.c) and after
> printing the message it appears to go back to the start of the main
> simplex solving loop.  So I'm thinking that maybe it was able to
> recover from the problem and proceeded to find an accurate optimal
> solution.  Is this case?  Does the message mean that it was unable to
> find an accurate solution or does the message simply supply some
> information that can safely be ignored?
> 

This message just informs you that the simplex solver detects that the
current basic solution became infeasible due to excessive round-off
errors. In this case the solver automatically switches to the phase I to
recover feasibility and then continues the search. If the solver routine
returns 0, the solution can be considered as accurate within the working
precision used. Note that you can use the routine glp_check_kkt to check
if the solution satisfies to the feasibility/optimality conditions.