Is the mailing Gilbert-Steiner problem convex?
Optimization and Control
2019-05-07 v4
Abstract
A convexification of the mailing version of the finite Gilbert problem for optimal networks is introduced. It is ia convex functional on the set of probability measures subject to the Wasserstein metric. The minimizer of this convex functional is a measure supported in a graph. If this graph is a tree (i.e contains no cycles) then this tree is also a minimum of the corresponding mailing Gilbert problem. A numerical algorithm for the implementation of the convexified Gilbert-mailing problem is also suggested, based on entropic regularization.
Cite
@article{arxiv.1901.10924,
title = {Is the mailing Gilbert-Steiner problem convex?},
author = {Gershon Wolansky},
journal= {arXiv preprint arXiv:1901.10924},
year = {2019}
}
Comments
In this version I recognised the possibility of cycles, so the result is conditioned on at the absence of such cycles