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Quadratically Regularized Optimal Transport on Graphs
Name
17m1132665.pdf
Description
Published version
Size
556.54 KB
Format
Adobe PDF
Checksum (MD5)
5a581eb4d58ad0ff8f6085f401a2802a
Author(s)
Essid, Montacer
Solomon, Justin
Date Issued
2018
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
© 2018 Society for Industrial and Applied Mathematics. Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to express challenging tasks involving matching supply to demand with minimal shipment expense; in discrete language, these become minimum-cost network flow problems. Regularization typically is needed to ensure uniqueness for the linear ground distance case and to improve optimization convergence. In this paper, we characterize a quadratic regularizer for transport with linear ground distance over a graph. We theoretically analyze the behavior of quadratically regularized graph transport, characterizing how regularization affects the structure of flows in the regime of small but nonzero regularization. We further exploit elegant second-order structure in the dual of this problem to derive an easily implemented Newton-type optimization algorithm.
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
10.1137/17M1132665
