The structure of the infinite models in integer programming
  The infinite models in integer programming can be described as the convex hull of some points or as the intersection of halfspaces derived from valid functions. In this paper we study the relationships between these two descriptions. Our results have implications for corner polyhedra. One consequence is that nonnegative, continuous valid functions suffice to describe corner polyhedra (with or without rational data). 
Amitabh Basu, Michele Conforti, Marco Di Summa, Joseph Paat
math.OC