  Given two disjoint convex polyhedra, we look for a best approximation pair
relative to them, i.e., a pair of points, one in each polyhedron, attaining the
minimum distance between the sets. Cheney and Goldstein showed that alternating
projections onto the two sets, starting from an arbitrary point, generate a
sequence whose two interlaced subsequences converge to a best approximation
pair. We propose a process based on projections onto the half-spaces defining
the two polyhedra, which are more negotiable than projections on the polyhedra
themselves. A central component in the proposed process is the
Halpern--Lions--Wittmann--Bauschke algorithm for approaching the projection of
a given point onto a convex set.
