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This research aims to explore the connections between c-cyclical monotonicity and optimal transport in classical and weak contexts.

June 23, 2026Open Access

A land of monotone plenty, bis repetita: from classical to weak optimal transport

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This research aims to explore the connections between c-cyclical monotonicity and optimal transport in classical and weak contexts.
Demonstrated the equivalence of optimality to non-negativity of transport cost on admissible perturbations.
Extended the c-cyclical monotonicity property to weak optimal transport via first-order conditions.
Revisited proofs for previously known results in classical optimal transport.
Showed that c-cyclical monotonicity characterizes optimal transport plans under specific assumptions.
Established a foundation for understanding optimality in weak transport scenarios.
Provided new insights into monotonicity concepts in both classical and weak optimal transport.

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Randomized trial reveals the relationship between optimality conditions in optimal transport problems, suggesting new insights.

Ehrlacher et al. (2026) studied this question.

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