Is the mailing Gilbert-Steiner problem convex?

Gershon Wolansky

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arXiv · 1901.10924

Is the mailing Gilbert-Steiner problem convex?

Gershon Wolansky

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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 $p-$ 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.

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BibTeX RIS

Gershon Wolansky. 2019-05-04. Is the mailing Gilbert-Steiner problem convex?. https://arxiv.org/abs/1901.10924

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