Santaló Geometry of Convex Polytopes
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909401959366656 |
|---|---|
| author | Pavlov, Dmitrii Telen, Simon |
| author_facet | Pavlov, Dmitrii Telen, Simon |
| contents | The Santaló point of a convex polytope is the interior point which leads to a polar dual of minimal volume. This minimization problem is relevant in interior point methods for convex optimization, where the logarithm of the dual volume is known as the universal barrier function. When translating the facet hyperplanes, the Santaló point traces out a semi-algebraic set. We describe and compute this geometry using algebraic and numerical techniques. We exploit connections with statistics, optimization and physics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Santaló Geometry of Convex Polytopes Pavlov, Dmitrii Telen, Simon Algebraic Geometry Optimization and Control 52B20, 52A40, 62R01, 65H14 The Santaló point of a convex polytope is the interior point which leads to a polar dual of minimal volume. This minimization problem is relevant in interior point methods for convex optimization, where the logarithm of the dual volume is known as the universal barrier function. When translating the facet hyperplanes, the Santaló point traces out a semi-algebraic set. We describe and compute this geometry using algebraic and numerical techniques. We exploit connections with statistics, optimization and physics. |
| title | Santaló Geometry of Convex Polytopes |
| topic | Algebraic Geometry Optimization and Control 52B20, 52A40, 62R01, 65H14 |
| url | https://arxiv.org/abs/2402.18955 |