Optimal Boundary Control of Diffusion on Graphs via Linear Programming
Published in Preprint (submitted), 2025
We propose a linear programming (LP) framework for steady-state diffusion and flux optimization on geometric networks. Boundary potentials act as controls that drive interior fluxes according to a linear network Laplacian. The resulting LP has polyhedral feasible set; we prove existence of a global minimizer under mild conditions (using recession cones and the Minkowski–Weyl decomposition) and identify several sufficient boundedness conditions. Numerical experiments on two large-scale real-world networks demonstrate stability, sign correctness, and flux conservation to machine precision.
Status: Submitted, 2025.
Recommended citation: H. Antil, R. Löhner, and F. Pérez. (2025). "Optimal Boundary Control of Diffusion on Graphs via Linear Programming." Preprint. arXiv:2511.03129.
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