Blocking and anti-blocking pairs of polyhedra

Some of the main notions and theorems about blocking pairs of polyhedra and antiblocking pairs of polyhedra are described. The two geometric duality theories conform in many respects, but there are certain important differences. Applications to various combinatorial extremum problems are discussed, and some classes of blocking and anti-blocking pairs that have been explicitly determined are mentioned.This paper was presented at the 7th Mathematical Programming Symposium 1970, The Hague, The Netherlands.