{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2507.09437",
  "author_total": 2,
  "authors": [
    {
      "name": "Luigi de Pascale"
    },
    {
      "name": "Paul Pegon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2he2zpbbbkmhc.bib",
  "cited_by": 0,
  "doi": "10.1142/s0219199726500719",
  "fulltext_url": null,
  "id": "2he2zpbbbkmhc",
  "issns": [
    "0219-1997",
    "0219-1997"
  ],
  "landing_url": "https://inria.hal.science/hal-05160124v3",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.shs"
    ],
    [
      "hal",
      "1.shs.eco"
    ],
    [
      "openalex",
      "1703|Optimization and Variational Analysis"
    ]
  ],
  "openalex": "W4414627530",
  "pdf_url": "https://inria.hal.science/hal-05160124/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": "World Scientific Publishing",
  "ris": "https://research.draconitic.com/paper/2he2zpbbbkmhc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:57Z",
      "native_id": "hal-05160124",
      "source": "hal",
      "url": "https://inria.hal.science/hal-05160124v3"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "A Rockafellar theorem for cyclically quasi-monotone maps: The regular non-vanishing case",
  "title_text": "A Rockafellar theorem for cyclically quasi-monotone maps: The regular non-vanishing case",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:57Z",
  "url": "https://research.draconitic.com/paper/2he2zpbbbkmhc",
  "venue": "Communications in Contemporary Mathematics",
  "versions": []
}