Numerical robustness of high-dimensional Convex Hull selection

Determine whether additional scale-aware numerical criteria are required for the facet-based high-dimensional Convex Hull construction in FINALLY, particularly for point sets with very small but valid hull volumes.

Background

FINALLY uses a high-dimensional Convex Hull objective within a greedy dataset-set selection procedure. The thesis reports that the final evaluation did not exercise every geometric path supported by the implementation, especially cases involving more points than the minimum required for their intrinsic rank. Such cases may expose numerical issues, including incorrectly computed zero hull volumes that could affect non-diverse optimization. The unresolved issue is whether additional scale-aware numerical criteria are needed to make the facet-based construction robust in these cases.