Re: [Help-glpk] infeasible ray

[Andrew Makhorin]

> And what about, when the problem is primal-dual infeasible. Then
> there is a primal ray and also a dual ray, however there is not
> feasible solution for both problems.

Ray assumes unboundedness, which, in turn, assumes feasibility (either
in the primal or dual space).

> I have a function, which computes the ray, if glpk finds out the
> problem is unbounded in the second phase, but I looking for a
> solution, when I can build the ray without building a new problem
> object or modify the current, if the first phase failed. I have an
> idea, but I do not know if it is realizable. I think the failed
> first phase gives back a primal solution, which violations are
> minimized, and the basis remain the same as the end of the first
> phase. I think with some API function it is possible to calculate a
> dual solution from the primal one. Do you think, is it possible or
> not?

Your question is not quite clear. Which analysis do you need to
perform? Note that you always can make lp primal feasible replacing
rhs's in all constraints and bounds of all variables by zeros that
does not affect the dual polyhedron. Similarly, you can make lp dual
feasible replacing all objective coefficients by zeros that does not
change the primal polyhedron.