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

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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 à 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 will allow us to prove the existence and to describe the solutions for both the primal optimization problem and its Eulerian counterpart.

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Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Samer Dweik, Nassif Ghoussoub & Aaron Zeff Palmer

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  1. Samer Dweik
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  2. Nassif Ghoussoub
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  3. Aaron Zeff Palmer
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Correspondence to Samer Dweik.

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In the published article “Optimal Controlled Transports with Free End Times Subject to Import/Export Tariffs”, incorrect pagination is spotted. In the PDF of this article, pages 482–507 were incorrectly numbered.

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Dweik, S., Ghoussoub, N. & Palmer, A.Z. Optimal Controlled Transports with Free End Times Subject to Import/Export Tariffs. J Dyn Control Syst 26, 481–507 (2020). https://doi.org/10.1007/s10883-019-09458-1

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  • DOI: https://doi.org/10.1007/s10883-019-09458-1

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