Characterizations of Faces of Convex Sets in Infinite-dimensional Vector Spaces
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915335393771520 |
|---|---|
| author | Gorokhovik, Valentin V. |
| author_facet | Gorokhovik, Valentin V. |
| contents | In the paper three different characterizations of faces of convex sets, belonging to infinite-dimensional real vector spaces, are presented. The first one is formulated in the terms of generalized semispaces, the second -- in the terms of compatible complete (total) preorders, and the third -- in the terms of step-affine functions. All three characterization are equivalent each other and extend to infinite-dimensional vector spaces the lexicographical characterization of faces established in finite-dimensional settings by Martinez-Legaz J.-E. (Acta Mathematica Vietnamica. 1997. Vol. 22, No.~1, P. 207--211). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08742 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterizations of Faces of Convex Sets in Infinite-dimensional Vector Spaces Gorokhovik, Valentin V. Optimization and Control 52A05, 52A99 In the paper three different characterizations of faces of convex sets, belonging to infinite-dimensional real vector spaces, are presented. The first one is formulated in the terms of generalized semispaces, the second -- in the terms of compatible complete (total) preorders, and the third -- in the terms of step-affine functions. All three characterization are equivalent each other and extend to infinite-dimensional vector spaces the lexicographical characterization of faces established in finite-dimensional settings by Martinez-Legaz J.-E. (Acta Mathematica Vietnamica. 1997. Vol. 22, No.~1, P. 207--211). |
| title | Characterizations of Faces of Convex Sets in Infinite-dimensional Vector Spaces |
| topic | Optimization and Control 52A05, 52A99 |
| url | https://arxiv.org/abs/2506.08742 |