  A convex partition of a point set P in the plane is a planar partition of the
convex hull of P with empty convex polygons or internal faces whose extreme
points belong to P. In a convex partition, the union of the internal faces give
the convex hull of P and the interiors of the polygons are pairwise disjoint.
Moreover, no polygon is allowed to contain a point of P in its interior. The
problem is to find a convex partition based on the minimum number of internal
faces. The problem has been shown to be NP-Hard and was recently used in the
CG:SHOP Challenge 2020. We propose a new integer linear programming (IP)
formulation that considerably improves over the existing one. It relies on the
representation of faces as opposed to segments and points. A number of
geometric properties are used to strengthen it. Data sets of 100 points are
easily solved to optimality and the lower bounds provided by the model can be
computed up to 300 points.
