Generating Function Algorithms and Software for Integer Optimization

by Jesus De Loera

in the 1990s A. Barvinok proposed rational generating functions as the ideal 
fast data structure for representing or encoding lattice points inside 
polyhedra. In this talk we explain how rational functions (of various types) 
have found interesting use in integer optimization. In particular we discuss 
new linear integer programming and non-linear integer programming algorithms.

We also discuss the practical side of these algorithms. For example, 
the software {\tt LattE}, developed by the speakers group, has solved 
some very nasty knapsack problems within minutes of computation.