Re: [Bug-glpk] Dualp simplex method classifies an unbounded problem as "no primal feasible"

[Andrew Makhorin]

>> I am testing GLPK 4.36. I tried a test case that I have also used with
>> GLPK 4.19.
>  
>> Maximize 
>>        40 * x1 + 60 * x2
>> subject to
>>    0 <=     x1
>>    0 <=               x2
>>   70 <= 2 * x1 +      x2
>>   40 <=     x1 +      x2
>>   90 <=     x1 +  3 * x2
>  
>> This problem is primal feasible. It is unbounded. 
> 
>> In GLPK 4.19, after running the dualp simplex method (GLP_DUALP), the
>> solution status is unbounded (GLP_UNBND). This is what I expected.
> 
>> In GLPK 4.36, after running the dualp simplex method (GLP_DUALP), the
>> solution status is infeasible (GLP_INFEAS). Why doesn't the code find a
>> feasible solution?
> 
> Thank you for your report.
> 
> This is not a bug. Glpk 4.19 has no phase I dual simplex, so if the
> initial basis passed to the simplex solver is dual infeasible, it
> automatically switches to the primal simplex, and it detects
> unboundedness. In glpk 4.36 the dual simplex implements both phases
> I and II, and if you specify GLP_DUALP, the phase I dual simplex attempts
> to find a dual feasible solution; it does not exist as your instance is
> unbounded, so it reports the status of the last basic solution reached,
> which is neither primal nor dual feasible.

You may check the dual status reported by glp_get_dual_stat, which
must be GLP_NOFEAS in your case (no dual feasible solution exists);
that means that the problem is either unbounded or has no primal
feasible solution.