Error in the 3D case with thin triangle like obstacles

[tardani95]

Problem setup

I am trying to approximate the largest convex region in the 3D case, where the obstacles are thin triangles, and they are together, creating a 3D concave surface. Like in this picture:

I provide the iris algorithm an initial point that is certainly inside of the surface.

Issue 1

I receive 1 out of 10 optimizations with the following errors:

1. MSK_RES_ERR_LOWER_BOUND_IS_A_NAN: The lower bound specified is not a number (nan).
2. Inner ellipsoid problem is infeasible (this likely means that the polyhedron has no interior)

Does somebody know what can cause the problem?

Issue 2 - Solved

Another issue is that sometimes, the approximated polyhedron collapses, although the ellipse grows (iteration 3):

The collapsing polyhedron comes from the numerically unstable cddlib, the half-space representation is correct.