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arXiv · 1903.02126

Optimal Controlled Transports with Free End Times Subject to Import/Export Tariffs

Samer Dweik·Nassif Ghoussoub·Aaron Zeff Palmer
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Abstract

We analyze controlled mass transportation plans with free end-time that minimize the transport cost induced by the generating function of a Lagrangian within a bounded domain, in addition to costs incurred as export and import tariffs at entry and exit points on the boundary. We exhibit a dual variational principle \`a la Kantorovich, that takes into consideration the additional tariffs. We then show that the primal optimal transport problem has an equivalent Eulerian formulation whose dual involves the resolution of a Hamilton-Jacobi-Bellman quasi-variational inequality with non-homogeneous boundary conditions. This allows us to prove existence and to describe the solutions for both the primal optimization problem and its Eulerian counterpart.

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Samer Dweik, Nassif Ghoussoub, Aaron Zeff Palmer. 2019-03-06. Optimal Controlled Transports with Free End Times Subject to Import/Export Tariffs. https://arxiv.org/abs/1903.02126

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