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Overlapping Schwarz Scheme for Linear-Quadratic Programs ...
[Submitted on 6 Oct 2025 (v1), last revised 10 Sep 2026 (this ve · 2025-10-06 · via cs.DC updates on arXiv.org

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Abstract: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.

Submission history

From: Sen Na [view email]
[v1] Mon, 6 Oct 2025 04:28:39 UTC (1,430 KB)
[v2] Sun, 12 Oct 2025 17:55:21 UTC (1,430 KB)
[v3] Thu, 10 Sep 2026 22:32:48 UTC (1,456 KB)