Granular optimization: An approach to function optimization

Finding a function that minimizes a functional is common problem, e.g., determining the feedback control law for a system. However, it remains to be a challenge due to the large and structureless search space. In this paper, we present a search algorithm, granular optimization, to deal with this type of problems under some mild constraints. The algorithm is tested on two different problems. One of them is the well-known Witsenhausen counterexample (1968). On the counterexample, the result from our automated algorithm comes close to the currently known best solution, which involves much human intervention. This shows the potential usefulness of the algorithm in more general problems