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We propose a fast temporal decomposition procedure for solving long-horizonnonlinear dynamic programs. The core of the procedure is sequential quadraticprogramming (SQP) that utilizes a differentiable exact augmented Lagrangian asthe merit function. Within each SQP iteration, we approximately solve theNewton system using an overlapping temporal decomposition strategy. We showthat the approximate search direction is still a descent direction of theaugmented Lagrangian, provided the overlap size and penalty parameters aresuitably chosen, which allows us to establish the global convergence. Moreover,we show that a unit stepsize is accepted locally for the approximate searchdirection, and further establish a uniform, local linear convergence overstages. This local convergence rate matches the rate of the recent Schwarzscheme by Na et al., 2022. However, the Schwarz scheme has to solve nonlinearsubproblems to optimality in each iteration, while we only perform a singleNewton step instead. Numerical experiments validate our theories anddemonstrate the superiority of our method.

A Fast Temporal Decomposition Procedure for Long-horizon Nonlinear Dynamic Programming