The search for Bell inequalities is a famously hard problem. My collaborators and I have found a new approach to the problem which allows us to certify nonlocality in bipartite scenarios with up to 42 measurement settings and improving long standing bounds on Grothendieck's constant KG(3).
The general problem is called the separation problem. Given a point, we would like to decide if it is inside a convex set (the local hidden variable polytope) and if not provide a separating hyperplane (a Bell inequality). We solve the separation problem using an oracle to a sometime easier problem - that of optimising a linear functional over the convex set. Our approach gives a new theoretical and practical reduction that performs particularly well on large scale problems.