Full Text: PDF
DOI: 10.23952/cot.2026.20
Received January 20, 2025; Accepted March 4, 2025; Published online February 14, 2026
Abstract. This paper discusses an optimal control design for data transport and exchange via domain boundaries. The mathematical model is governed by the transport equations which are driven by the incompressible velocity fields. The objective is to optimize the density distributions of the data to the desired ones through active control of the velocity for transporting data on a portion of the domain boundaries. We provide a rigorous proof of existence of an optimal control and establish the Gâteaux differentiability of the objective functional with respect to the boundary control inputs. Finally, we derive the first-order optimality conditions for solving such an optimal solution using a variational inequality.
How to Cite this Article:
D.O. Adu, A.J. Brower, W. Hu, Z. Shen, Boundary control for optimal data transport, Commun. Optim. Theory 2026 (2026) 20.