Alternating direction algorithms for solving Hamilton-Jacobi-Bellman equations

We focus on numerically solving a typical type of Hamilton-Jacobi-Bellman (HJB) equations arising from a class of optimal controls with a standard multidimensional diffusion model. Solving such an equation results in the value function and an optimal feedback control law. The Bellman's curse of dimensionality seems to be the main obstacle to applicability of most numerical algorithms for solving HJB. We decompose HJB into a number of lower-dimensional problems, and discuss how the usual alternating direction method can be extended for solving HJB. We present some convergence results, as well as preliminary experimental outcomes.This research was funded in part by an RGC grant from the University of Alabama.