A Fast Temporal Decomposition Procedure for Long-

• 成果类型: Article
• 署名作者: Na, Sen; Anitescu, Mihai; Kolar, Mladen
• 署名单位: University of California System; University of California Berkeley; University of California System; University of California Berkeley; United States Department of Energy (DOE); Argonne National Laboratory; University of Chicago
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• 发表日期: 2024
• 页码: 1012-1044
• 关键词: quickest detection problems; statistical arbitrage; EQUATIONS

摘要

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 step size 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 (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.