Overlapping Schwarz Scheme for Linear-Quadratic Programs in Continuous Time
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918159112470528 |
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| author | Zhao, Hongli Anitescu, Mihai Na, Sen |
| author_facet | Zhao, Hongli Anitescu, Mihai Na, Sen |
| contents | We present an optimize-then-discretize framework for solving linear-quadratic optimal control problems (OCP) governed by time-inhomogeneous ordinary differential equations (ODEs). Our method employs a modified overlapping Schwarz decomposition based on the Pontryagin Minimum Principle, partitioning the temporal domain into overlapping intervals and independently solving Hamiltonian systems in continuous time. We demonstrate that the convergence is ensured by appropriately updating the boundary conditions of the individual Hamiltonian dynamics. The cornerstone of our analysis is to prove that the exponential decay of sensitivity (EDS) exhibited in discrete-time OCPs carries over to the continuous-time setting. Unlike the discretize-then-optimize approach, our method can flexibly incorporate different numerical integration methods for solving the resulting Hamiltonian two-point boundary-value subproblems, including adaptive-time integrators. A numerical experiment on a linear-quadratic OCP illustrates the practicality of our approach in broad scientific applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04478 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Overlapping Schwarz Scheme for Linear-Quadratic Programs in Continuous Time Zhao, Hongli Anitescu, Mihai Na, Sen Optimization and Control Computational Engineering, Finance, and Science Distributed, Parallel, and Cluster Computing Numerical Analysis Dynamical Systems We present an optimize-then-discretize framework for solving linear-quadratic optimal control problems (OCP) governed by time-inhomogeneous ordinary differential equations (ODEs). Our method employs a modified overlapping Schwarz decomposition based on the Pontryagin Minimum Principle, partitioning the temporal domain into overlapping intervals and independently solving Hamiltonian systems in continuous time. We demonstrate that the convergence is ensured by appropriately updating the boundary conditions of the individual Hamiltonian dynamics. The cornerstone of our analysis is to prove that the exponential decay of sensitivity (EDS) exhibited in discrete-time OCPs carries over to the continuous-time setting. Unlike the discretize-then-optimize approach, our method can flexibly incorporate different numerical integration methods for solving the resulting Hamiltonian two-point boundary-value subproblems, including adaptive-time integrators. A numerical experiment on a linear-quadratic OCP illustrates the practicality of our approach in broad scientific applications. |
| title | Overlapping Schwarz Scheme for Linear-Quadratic Programs in Continuous Time |
| topic | Optimization and Control Computational Engineering, Finance, and Science Distributed, Parallel, and Cluster Computing Numerical Analysis Dynamical Systems |
| url | https://arxiv.org/abs/2510.04478 |