Approximating the maximum of a polynomial over a polytope: Handelman   decomposition and continuous generating functions
  We investigate a way to approximate the maximum of a polynomial over a polytopal region by using Handelman's polynomial decomposition and continuous multivariate generating functions. The maximization problem is NP-hard, but our approximation methods will run in polynomial time when the dimension is fixed. 
Jes\'us De Loera and Brandon Dutra and Matthias K\"oppe
math.OC