Non-linear optimization in theory and practice

"Consolidation of farming by means of combinatorial optimization". Using
a set partioning approach we are able to propose reallocations of land
that could dramatically enhance the cost structure of the farmers.

Looking at integer linear programs from a more theoretical point of view
we are interested in the following question: Normally, we are not
guaranteed the existence of an integral optimal point once our integral
linear program is relaxed by dropping the integrality constraints.
However, can we choose a proper objective function that does so?

This question is answered for some relaxations of the stable set polytope
and, in a sense surprisingly, it is closely related to the computation of
different geometric functional of convex bodies.