I have a convex polytope described by the intersection of a hypercube and two parallel lower and upper hyperplanes cutting through the hypercube. I want to find the projection of a point onto the polytope.
I read the question Projection of a point onto a convex polyhedra and see that the general problem of finding a projection onto a convex polytope can be solved with quadratic programming.
However, taken alone, projection onto a hypercube or a hyperplane is trivial. For the hypercube, each dimension is defined by a lower+upper bounds and we just pull each dimension within those bounds, which take $O(n)$ time in $n$ dimensions. For the hyperplane just find the projection onto it.
So I'm wondering whether there is simpler method for finding such a projection, maybe somehow combining the two independent projections.