A Rockafellar Theorem for cyclically quasi-monotone maps: the regular non-vanishing case
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908532616462336 |
|---|---|
| author | De Pascale, Luigi Pegon, Paul |
| author_facet | De Pascale, Luigi Pegon, Paul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Rockafellar Theorem for cyclically quasi-monotone maps: the regular non-vanishing case De Pascale, Luigi Pegon, Paul Optimization and Control Functional Analysis Primary: 47H05, Secondary: 49Q22, 47N10 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. |
| title | A Rockafellar Theorem for cyclically quasi-monotone maps: the regular non-vanishing case |
| topic | Optimization and Control Functional Analysis Primary: 47H05, Secondary: 49Q22, 47N10 |
| url | https://arxiv.org/abs/2507.09437 |