{"ID":2895104,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.09437","arxiv_id":"2507.09437","title":"A Rockafellar Theorem for cyclically quasi-monotone maps: the regular non-vanishing case","abstract":"We study the connection between cyclic quasi-monotonicity and quasi-convexity, focusing on whether every cyclically quasi-monotone (possibly multivalued) 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 $\\mathscr{C}^1$-regular, 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 $L^\\infty$ optimal transport. Finally, we present explicit constructions and examples, highlighting the main challenges that arise in the general case.","short_abstract":"We study the connection between cyclic quasi-monotonicity and quasi-convexity, focusing on whether every cyclically quasi-monotone (possibly multivalued) 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 $...","url_abs":"https://arxiv.org/abs/2507.09437","url_pdf":"https://arxiv.org/pdf/2507.09437v2","authors":"[\"Luigi De Pascale\",\"Paul Pegon\"]","published":"2025-07-13T00:24:30Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.FA\"]","methods":"[]","has_code":false}