重庆理工大学学报2025，Vol.39Issue(17)：225-231,7.DOI:10.3969/j.issn.1674-8425(z).2025.09.028
一类用于求解抛物最优控制问题的时间并行算法
A parallel in time algorithm for solving parabolic optimal control problems
摘要
Abstract
In recent years,seeking the optimal control has gained keen academic interest.Among all the algorithms,the multiple shooting method effectively addresses optimal control problems governed by ordinary differential equations.However,some difficulties arise when applying this method to problems governed by partial differential equations.This paper proposes a novel time-parallel approach.First,the original problem is reformulated as an equivalent one with equality constraints by introducing auxiliary variables.Then,the augmented Lagrangian method is integrated with a conjugate gradient method to develop an efficient algorithm.The gradient of the augmented Lagrangian function is derived,and its parallel computation is discussed.Finally,the efficiency and accuracy of the proposed algorithm are validated through numerical experiments.关键词
多重打靶方法/抛物方程/增广拉格朗日算法/共轭梯度算法/梯度计算/最优控制/并行计算/扰动分析Key words
multiple shooting/parabolic equations/augmented Lagrangian method/conjugate gradient method/gradient computing/optimal control/parallel computing/perturbation analysis分类
数理科学引用本文复制引用
高燕飞,张月琴..一类用于求解抛物最优控制问题的时间并行算法[J].重庆理工大学学报,2025,39(17):225-231,7.基金项目
国家自然科学基金项目(11771321) （11771321）
山西省教育厅教学改革与实践研究重点项目(202302013) （202302013）
