  The aim of this paper is to investigate from the numerical point of view the
possibility of coupling the Hamilton-Jacobi-Bellman (HJB) equation and
Pontryagin's Minimum Principle (PMP) to solve some control problems. A rough
approximation of the value function computed by the HJB method is used to
obtain an initial guess for the PMP method. The advantage of our approach over
other initialization techniques (such as continuation or direct methods) is to
provide an initial guess close to the global minimum. Numerical tests involving
multiple minima, discontinuous control, singular arcs and state constraints are
considered. The CPU time for the proposed method is less than four minutes up
to dimension four, without code parallelization.
