This problem arose in a computer vision hobby project.
Say I have two sets of points in three dimensional Cartesian space: A and B.
The problem I would like to solve is to find the convex hull V of a subset of A that maximizes $|\{x|x \in A \wedge x \in V\}| - |\{x|x \in B \wedge x \in V\}|$, preferably in polynomial time.
If the convex hulls of A and B are disjoint then there is no problem. The case I would like help with is when some points from set B may fall inside the convex hull of A.