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A note on the c-monotonicity in optimal transport with capacity constraints
Published 28 Aug 2025 in math.OC | (2508.20428v1)
Abstract: This paper studies the geometry of the optimizer for the optimal transport problem with capacity constraints. We introduce the concept of c-capacity monotonicity, which is a generalization of c-cyclical monotonicity in optimal transport. We show that the optimizer of the optimal transport problem with capacity constraints is c-capacity monotone.
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