Zonotope membership test using simplex

[mforets]

Closes #246.

[schillic]

I do not understand what happens here. I see that you add one dimension for the objective function, but why does the solution have to be optimal? Can you add some more documentation what happens here?

[schillic]

one(N) resp. zero(N) (also below)
In fact, instead of fill you can use zeros(N, p), right? (same for ones and also below)
Does this always result in the correct dimensions, for any n and p? It is not easy to read for me...

[schillic]

not sure if there is a type-parametric Inf

[mforets]

N(Inf) should do it

[schillic]

return immediately?

[schillic]

What does "Infeasible of Unboudned" mean?
also a typo

[mforets]

infeasible means that there is no solution satisfying the constraints; unbounded if the feasible set is unbounded towards the direction of descent of the gradient of the objective function (but this is not the case in this instance since we take min x0 and 0<=x0<=infty, so it will return infeasible if the membership test fails.)

[schillic]

So it should be "if" instead of "of"?

[mforets]

yes, thanks

[mforets]

I do not understand what happens here. I see that you add one dimension for the objective function, but why does the solution have to be optimal? Can you add some more documentation what happens here?

i improved the docstring (and removed the previous one, i didn't see that it was above!)

for the type-parametric issue, i would have to investigate it further how we can enable this, since the computations ultimately relies on the LP solver backend used.

[schillic]

Thanks. I suggest to just test what happens when you input a Zonotope{Rational{Int}}. If it works, then we can leave it as is. Otherwise we should at least crash with a clear explanation.

[schillic]

"optional"

[schillic]

Is there a reason why you use fill instead of zeros/ones?

[mforets]

it works using method=:Exact; compare:

julia>     lp = linprog(obj, A, sense, b, lbounds, ubounds, GLPKSolverLP(method=:Exact))
glp_exact: 3 rows, 3 columns, 3 non-zeros
GNU MP bignum library is being used
      0:   infsum =                    0.2   (0)
      2:   infsum =                      0   (0)
*     2:   objval =                      0   (0)
*     2:   objval =                      0   (0)
OPTIMAL SOLUTION FOUND
MathProgBase.HighLevelInterface.LinprogSolution(:Optimal, 0.0, [0.0, 0.0, 0.0], Dict{Any,Any}(Pair{Any,Any}(:lambda, [0.0, 0.0, 0.0]),Pair{Any,Any}(:redcost, [1.0, 0.0, 0.0])))

and

julia>     lp = linprog(obj, A, sense, b, lbounds, ubounds, GLPKSolverLP(method=:Simplex))
MathProgBase.HighLevelInterface.LinprogSolution(:Optimal, 0.0, [0.0, 0.0, 0.0], Dict{Any,Any}(Pair{Any,Any}(:lambda, [0.0, 0.0, 0.0]),Pair{Any,Any}(:redcost, [1.0, 0.0, 0.0])))

i wouldn't expect that for the former case it returns values in Float64 though. but clearly glp_exact is triggered.

[mforets]

Is there a reason why you use fill instead of zeros/ones?

no

[schillic]

i wouldn't expect that for the former case it returns values in Float64 though. but clearly glp_exact is triggered.

Yes, that looks strange, but maybe it can automatically work with floats if possible for efficiency.