On c -cyclical monotonicity for optimal transport problem with Coulomb cost

It is proved that c -cyclical monotonicity is a sufficient condition for optimality in the multi-marginal optimal transport problem with Coulomb repulsive cost. The notion of c -splitting set and some mild regularity property are the tools. The result may be extended to Coulomb like costs.

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Bibliographic Details
Published in:European journal of applied mathematics 2019-12, Vol.30 (6), p.1210-1219
Main Author: DE PASCALE, LUIGI
Format: Article
Language:English
Subjects:
Applied mathematics
Optimization
Transport
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Summary:It is proved that c -cyclical monotonicity is a sufficient condition for optimality in the multi-marginal optimal transport problem with Coulomb repulsive cost. The notion of c -splitting set and some mild regularity property are the tools. The result may be extended to Coulomb like costs.
ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792519000111