Optimality certificates for convex minimization and Helly numbers
  We consider the problem of minimizing a convex function over a subset of R^n that is not necessarily convex (minimization of a convex function over the integer points in a polytope is a special case). We define a family of duals for this problem and show that, under some natural conditions, strong duality holds for a dual problem in this family that is more restrictive than previously considered duals. 
Amitabh Basu and Michele Conforti and G\'erard Cornu\'ejols and Robert   Weismantel and Stefan Weltge
math.OC