Re: [Help-glpk] glpk status NOFEAS INFEAS

[Andrew Makhorin]

> When I use primal simplex method to solve an unbounded LP problem.
> Checking status gives this:
>         glp_get_status() returns GLP_UNBND,
>         glp_get_prim_stat() returns GLP_FEAS,
>         glp_get_dual_stat() returns GLP_NOFEAS.
> Then using dual simplex method to solve the same problem, I got
>         glp_get_status() returns GLP_INFEAS,
>         glp_get_prim_stat() returns GLP_INFEAS,
>         glp_get_dual_stat() returns GLP_NOFEAS.
> 
> Next, I use primal simplex method to solve another LP which is the
> dual problem of the previous LP.
> Checking status gives this:
>         glp_get_status() returns GLP_NOFEAS,
>         glp_get_prim_stat() returns GLP_NOFEAS,
>         glp_get_dual_stat() returns GLP_INFEAS.
> Thent, I use dual simplex method, and I got
>         glp_get_status() returns GLP_NOFEAS, 
>         glp_get_prim_stat() returns GLP_NOFEAS,
>         glp_get_dual_stat() returns GLP_FEAS.
> I'd like to ask
> (a) What is the difference between GLP_NOFEAS and GLP_INFEAS ?

GLP_INFEAS returned by glp_get_prim_stat or glp_get_dual_stat simply
means that the current basis is primal (dual) infeasible. GLP_NOFEAS 
is a stronger status meaning that the problem has no primal (no dual)
feasible solution, that is, the minimal sum of primal (dual)
infeasibilities is non-zero for such problem. 

For more details please see the glpk reference manual.

> (b) How can I check wheter the primal or dual solution is unbounded ?
> 

Primal (dual) solution is unbounded if the problem has a primal (dual)
feasible solution and no dual (primal) feasible solution.