A new separation algorithm, finding high dimensional Bell inequities and how to improve the bounds on Grothendieck’s constant

I’ll introduce a new algorithm for finding separating hyperplanes of convex sets. It uses as an oracle a convex optimization solver which for some problems (such as characterising local models) is easy. There are two exciting applications. We are able to significantly out-perform previous algorithms for finding Bell inequalities in high dimensions (say a large number of measurement settings) that were based on linear programming techniques. The second (related) example is that we improve the bounds on Grothendieck’s constant from the theory of Banach spaces.