A Rockafellar theorem for cyclically quasi-monotone maps: The regular non-vanishing case

Luigi de Pascale () and Paul Pegon ()
Additional contact information
Luigi de Pascale: DiMal - Dipartimento di Matematica e Informatica [Firenze] - UniFI - Università degli Studi di Firenze = University of Florence = Université de Florence
Paul Pegon: MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales - CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique - Centre Inria de Paris - Inria - Institut National de Recherche en Informatique et en Automatique, CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

Abstract: In this paper, we study the connection between cyclic quasi-monotonicity and quasi-convexity, focusing on whether every cyclically quasi-monotone (possibly multi-valued) map is included in the normal cone operator of a quasi-convex function, in analogy with Rockafellar's theorem for convex functions. We provide a positive answer for locally Lipschitz, non-vanishing maps in any dimension, as well as for general multi-maps in dimension 1. We further discuss connections to revealed preference theory in economics and to L᪲ optimal transport. Finally, we present explicit constructions and examples, highlighting the main challenges that arise in the general case.

Keywords: revealed preference; convex analysis; L ∞ optimal transport; optimal transport; quasi-convexity; quasi-monotonicity (search for similar items in EconPapers)
Date: 2026-09-22
New Economics Papers: this item is included in nep-mac
Note: View the original document on HAL open archive server: https://inria.hal.science/hal-05160124v3
References: Add references at CitEc
Citations:

Published in Communications in Contemporary Mathematics, inPress, ⟨10.1142/S0219199726500719⟩

Downloads: (external link)
https://inria.hal.science/hal-05160124v3/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05160124

DOI: 10.1142/S0219199726500719

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().