I’m quite new to Julia and try to solve the following problem efficiently:

For a given bounded polyhedron (by the linear equations Ax = 0 and bounds on x), I have to check whether it contains a non-negative integral point except the zero vector (which is always feasible). So far, I’m using JuMP to maximize something like sum(x) and check if the optimal value is 0 or greater than 0.

Now I’ve found the Polyhedra package, but no function that does what I need… Has anyone an idea how this can be implemented more efficiently than I’ve described above?

Yeah right, I can omit the objective function and add a constraint to avoid the origin, thanks!

Adittional question: For some instances I obtain the termination_statusDUAL_INFEASIBLE. Is there any chance to decided feasibility of the primal anyway?

What solver are you using? DUAL_INFEASIBLE suggest that the problem is unbounded, but that shouldn’t matter for a feasibility problem? Maybe you can provide a bounding box as well?

I’m using CPLEX and Gurobi with the same result (DUAL_INFEASIBLE). That was also my first thought but the problem is bounded… I can offer the example below (sorry, I haven’t found a smaller matrix where this phenomenon occur).

If I switch to GLPK, I obtain warnings like Warning: numerical instability (primal simplex, phase I) and Warning: numerical instability (primal simplex, phase II), but the termination status is now OPTIMAL in this specific example… I don’t really get it.

That bound is rather wide. It evaluates to > 5e21 for me. I’m guessing that most solvers consider this value “infinite”, hence the variables are actually unbounded.

Also, your example still has the @objective set.

When reading the first post, I was thinking of binary variables, for some reason.

When calling isempty on a polyhedron with Polyhedra, it solves the same linear problem with JuMP than the one you are formulating in JuMP so you won’t gain anything by using Polyhedra, it’s the same for the solvers