{
  "abstract": "Rockafellar showed that every cyclically monotone operator is contained in the subdifferential of a convex function, and characterized the maximal ones. We establish the quasi-convex analogue of this theorem, with no assumption on the operator: in any separable Banach space, a setting we show to be sharp, every cyclically quasi-monotone operator is contained in the normal cone operator of a quasi-convex function. In finite dimension, we characterize maximal cyclically quasi-monotone operators and show that they are maximal quasi-monotone. Unlike in the convex case, the potential is not unique, and we build it from a preference relation obtained through successive preorders. As applications, we extend Afriat's theorem on revealed preferences in economics to infinite data sets, and obtain Kantorovich-type potentials for a supremal optimal transport problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20542",
  "author_total": 2,
  "authors": [
    {
      "name": "Luigi de Pascale"
    },
    {
      "name": "Paul Pegon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/235dt9zhms6fm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20542",
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  "id": "235dt9zhms6fm",
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  "landing_url": "https://inria.hal.science/hal-05800300v1",
  "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": "CC0-1.0",
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      "math.FA"
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  "openalex": "W7222160141",
  "pdf_url": "https://inria.hal.science/hal-05800300/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/235dt9zhms6fm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:57Z",
      "native_id": "hal-05800300",
      "source": "hal",
      "url": "https://inria.hal.science/hal-05800300v1"
    },
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20542",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20542"
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  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "The quasi-convex Rockafellar theorem",
  "title_text": "The quasi-convex Rockafellar theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/235dt9zhms6fm",
  "venue": "HAL",
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}