Projecting points on the convex hull

We discuss the problem of projecting points on their convex hull. Points in the interior of the convex hull are moved outwards to the boundary of the convex hull. While finding the convex hull is a well treated problem, projecting each interior point on the convex hull is not. It is a harder problem, since each point has to be treated. We first discuss a solution approach in two dimensions, and then generalize it to three dimensions. After some significant improvements and changes, we arrive at efficient solutions method for the three dimensional case, using various column and/or constraint generation techniques