Convex sets approximable as the sum of a compact set and a cone
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917573136744448 |
|---|---|
| author | Dörfler, Daniel Löhne, Andreas |
| author_facet | Dörfler, Daniel Löhne, Andreas |
| contents | The class of convex sets that admit approximations as Minkowski sum of a compact convex set and a closed convex cone in the Hausdorff distance is introduced. These sets are called approximately Motzkin-decomposable and generalize the notion of Motzkin-decomposability, i.e. the representation of a set as the sum of a compact convex set and a closed convex cone. We characterize these sets in terms of their support functions and show that they coincide with self-bounded sets, i.e. sets contained in the sum of a compact convex set and a closed convex cone, if their recession cones are polyhedral but are more restrictive in general. In particular we prove that a set is approximately Motzkin-decomposable if and only if its support function has a closed domain relative to which it is continuous. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09026 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convex sets approximable as the sum of a compact set and a cone Dörfler, Daniel Löhne, Andreas Optimization and Control The class of convex sets that admit approximations as Minkowski sum of a compact convex set and a closed convex cone in the Hausdorff distance is introduced. These sets are called approximately Motzkin-decomposable and generalize the notion of Motzkin-decomposability, i.e. the representation of a set as the sum of a compact convex set and a closed convex cone. We characterize these sets in terms of their support functions and show that they coincide with self-bounded sets, i.e. sets contained in the sum of a compact convex set and a closed convex cone, if their recession cones are polyhedral but are more restrictive in general. In particular we prove that a set is approximately Motzkin-decomposable if and only if its support function has a closed domain relative to which it is continuous. |
| title | Convex sets approximable as the sum of a compact set and a cone |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2401.09026 |