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

arXiv: https://arxiv.org/abs/2107.11560 · HTML: https://mlsanity.com/paper/2107.11560/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2021.

## Built on by (most cited first, 2 of 2)

- [Constrained Optimization via Exact Augmented Lagrangian and Randomized Iterative Sketching](https://mlsanity.com/paper/2305.18379/) (2023)
- [Online Statistical Inference of Constrained Stochastic Optimization via Random Scaling](https://mlsanity.com/paper/2505.18327/) (2025)

## Abstract (arXiv)

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.