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.
On c -cyclical monotonicity for optimal transport problem with Coulomb cost / De Pascale L.. - In: EUROPEAN JOURNAL OF APPLIED MATHEMATICS. - ISSN 0956-7925. - ELETTRONICO. - (2019), pp. 1-10. [10.1017/S0956792519000111]
On c -cyclical monotonicity for optimal transport problem with Coulomb cost
De Pascale L.
2019
Abstract
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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