Qhull(Qhalf) interior point

Question

I am using qhull library for for computing the intersection of half spaces. Although this problem is a dual of convex hull problem, but as its input it needs an interior point of the intersection. As it is stated on their webpage, here, using linear programming we can find such a point. However, even for simple 2D cases, this LP problem does not have a bounded solution. Is there something wrong with the given instruction on the qhull website?

Answer 1

Well I found the answer myself! Yest the LP would be unbounded and we need to set an upper bound, depending on the context of the given problem.