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Duality theory for multi-marginal optimal transport with repulsive costs in metric spaces

Tapio RajalaAnna KausamoAugusto Gerolin

subject

Class (set theory)Control and OptimizationComputer Science::Information Retrieval010102 general mathematicsFOS: Physical sciencesContext (language use)Function (mathematics)Mathematical Physics (math-ph)01 natural sciences010101 applied mathematicsComputational MathematicsMetric spaceMathematics - Analysis of PDEsControl and Systems EngineeringOptimization and Control (math.OC)Bounded functionFOS: MathematicsApplied mathematicsDensity functional theoryLimit (mathematics)0101 mathematicsMathematics - Optimization and ControlMathematical PhysicsMathematicsAnalysis of PDEs (math.AP)

description

In this paper we extend the duality theory of the multi-marginal optimal transport problem for cost functions depending on a decreasing function of the distance (not necessarily bounded). This class of cost functions appears in the context of SCE Density Functional Theory introduced in "Strong-interaction limit of density-functional theory" by M. Seidl.

yearjournalcountryeditionlanguage
2018-05-02
https://dx.doi.org/10.48550/arxiv.1805.00880