The oriented mailing problem and its convex relaxation
Analysis of PDEs
2020-06-30 v2 Optimization and Control
Abstract
In this note we introduce a new model for the mailing problem in branched transportation in order to allow the cost functional to take into account the orientation of the moving particles. This gives an effective answer to [Problem 15.9] of the book "Optimal transportation networks" by Bernot, Caselles, and Morel. Moreover we define a convex relaxation in terms of rectifiable currents with group coefficients. With such approach we provide the problem with a notion of calibration. Using similar techniques we define a convex relaxation and a corresponding notion of calibration for a variant of the Steiner tree problem in which a connectedness constraint is assigned only among a certain partition of a given set of finitely many points.
Cite
@article{arxiv.1904.08246,
title = {The oriented mailing problem and its convex relaxation},
author = {Marcello Carioni and Andrea Marchese and Annalisa Massaccesi and Alessandra Pluda and Riccardo Tione},
journal= {arXiv preprint arXiv:1904.08246},
year = {2020}
}