  Presented is a method for efficient computation of the Hamilton-Jacobi (HJ)
equation for time-optimal control problems using the generalized Hopf formula.
Typically, numerical methods to solve the HJ equation rely on a discrete grid
of the solution space and exhibit exponential scaling with dimension. The
generalized Hopf formula avoids the use of grids and numerical gradients by
formulating an unconstrained convex optimization problem. The solution at each
point is completely independent, and allows a massively parallel implementation
if solutions at multiple points are desired. This work presents a primal-dual
method for efficient numeric solution and presents how the resulting optimal
trajectory can be generated directly from the solution of the Hopf formula,
without further optimization. Examples presented have execution times on the
order of milliseconds and experiments show computation scales approximately
polynomial in dimension with very small high-order coefficients.
