An algorithm for minimum cardinality generators of cones
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916502976856064 |
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| author | Mayer, Matthias Georg von der Warth, Fabian |
| author_facet | Mayer, Matthias Georg von der Warth, Fabian |
| contents | This paper presents a novel proof that for any convex cone, the size of conically independent generators is at most twice that of minimum cardinality generators. While this result is known for linear spaces, we extend it to general cones through a decomposition into linear and pointed components. Our constructive approach leads to a polynomial-time algorithm for computing minimum cardinality generators of finitely generated cones, improving upon existing methods that only compute conically independent generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01451 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An algorithm for minimum cardinality generators of cones Mayer, Matthias Georg von der Warth, Fabian Optimization and Control 90C25 This paper presents a novel proof that for any convex cone, the size of conically independent generators is at most twice that of minimum cardinality generators. While this result is known for linear spaces, we extend it to general cones through a decomposition into linear and pointed components. Our constructive approach leads to a polynomial-time algorithm for computing minimum cardinality generators of finitely generated cones, improving upon existing methods that only compute conically independent generators. |
| title | An algorithm for minimum cardinality generators of cones |
| topic | Optimization and Control 90C25 |
| url | https://arxiv.org/abs/2412.01451 |