  We propose a fast temporal decomposition procedure for solving long-horizon
nonlinear dynamic programs. The core of the procedure is sequential quadratic
programming (SQP) that utilizes a differentiable exact augmented Lagrangian as
the merit function. Within each SQP iteration, we approximately solve the
Newton system using an overlapping temporal decomposition strategy. We show
that the approximate search direction is still a descent direction of the
augmented Lagrangian, provided the overlap size and penalty parameters are
suitably chosen, which allows us to establish the global convergence. Moreover,
we show that a unit stepsize is accepted locally for the approximate search
direction, and further establish a uniform, local linear convergence over
stages. This local convergence rate matches the rate of the recent Schwarz
scheme by Na et al., 2022. However, the Schwarz scheme has to solve nonlinear
subproblems to optimality in each iteration, while we only perform a single
Newton step instead. Numerical experiments validate our theories and
demonstrate the superiority of our method.
