  The Symplectic Pontryagin method was introduced in a previous paper. This
work shows that this method is applicable under less restrictive assumptions.
Existence of solutions to the Symplectic Pontryagin scheme are shown to exist
without the previous assumption on a bounded gradient of the discrete dual
variable. The convergence proof uses the representation of solutions to a
Hamilton-Jacobi-Bellman equation as the value function of an associated
variation problem.

Numerical Analysis;Optimization and Control