The Witsenhausen counterexample: a hierarchical search approach for nonconvex optimization problems

The Witsenhausens counterexample (1968) is a difficult nonconvex functional optimization problem which has been outstanding for more than 30 years. Considerable amount of literature has been accumulated, but optimal solutions remain elusive. In this paper, we develop a framework that allows one to gain additional new insights to the properties of a better solution for a benchmark instance. Through our approach, we are able to zero in on a solution that is 13% better than the previously known best solution, and more than 54% better than previous results obtained by other authors. More importantly, we demonstrate that our approach, called hierarchical search, can be useful in general optimization problems.