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

Part of: Miscellaneous topics in calculus of variations and optimal control Existence theories Optimality conditions

Published online by Cambridge University Press:  23 May 2019

LUIGI DE PASCALE Open the ORCID record for LUIGI DE PASCALE [Opens in a new window]
LUIGI DE PASCALE*
Affiliation:
Universita degli Studi di Firenze, Dipartimento di Matematica ed Informatica, Viale Morgagni, 67/A, Firenze, 50134, Italy email: luigi.depascale@unifi.it
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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.

Keywords

Multi-marginal optimal transportationMonge–Kantorovich problemoptimality conditionc-cyclical monotonicity

MSC classification

Primary: 49J45: Methods involving semicontinuity and convergence; relaxation
Secondary: 49N15: Duality theory 49K30: Optimal solutions belonging to restricted classes
Type
Papers
Information
European Journal of Applied Mathematics , Volume 30 , Special Issue 6: Applied Optimal Transport , December 2019 , pp. 1210 - 1219
Copyright
© Cambridge University Press 2019 

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