Preprint
Inserted: 5 feb 2026
Last Updated: 22 feb 2026
Year: 2026
Abstract:
We consider the general tropical (max-plus) version of the classical Monge--Kantorovich optimal transportation problem. For this problem we show the existence of solutions, provide the formula for the optimal cost in terms of the data, and give explicit formulae for some solutions satisfying additional nice properties (e.g.\ maximal solutions). We further provide the relationship between this problem and the classical optimal transportation problems through the Large deviations principle, which can be considered a version of the Maslov dequantization tailored for such a problem. Finally, we provide some explicit examples of solutions and study the metric properties of the optimal cost.
Keywords: optimal transportation, tropical semiring, idempotent analysis
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