  In the last decade, copositive formulations have been proposed for a variety
of combinatorial optimization problems, for example the stability number
(independence number). In this paper, we generalize this approach to infinite
graphs and show that the stability number of an infinite graph is the optimal
solution of some infinite-dimensional copositive program. For this we develop a
duality theory between the primal convex cone of copositive kernels and the
dual convex cone of completely positive measures. We determine the extreme rays
of the latter cone, and we illustrate this theory with the help of the kissing
number problem.
