2021/07/24 by Sen Na, Mihai Anitescu, Na, Sen +3 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Advanced Optimization Algorithms Research #Dynamical Systems (math.DS) #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2107.11560
openalex publication_date 2021/07/24 · openalex created_date 2023/04/22 · openalex updated_date 2026/07/28
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.