The primary purpose of this note is to provide an instructional summary of the state of the art regarding cyclic monotonicity and related notions. We will also present how these notions are tied to optimality in the optimal transport (or Monge-Kantorovich) problem, even though cyclic monotonicity is simply a property of a set and can be studied on its own merit.
60 Years of Cyclic Monotonicity: a Survey / De Pascale L.; Kausamo A.; Wyczesany K.. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - STAMPA. - 35:(2025), pp. 399-430.
60 Years of Cyclic Monotonicity: a Survey
De Pascale L.;Kausamo A.;Wyczesany K.
2025
Abstract
The primary purpose of this note is to provide an instructional summary of the state of the art regarding cyclic monotonicity and related notions. We will also present how these notions are tied to optimality in the optimal transport (or Monge-Kantorovich) problem, even though cyclic monotonicity is simply a property of a set and can be studied on its own merit.
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