On Computing the Copositive Minimum and its Representatives
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916974583349248 |
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| author | Oertel, Alexander Schürmann, Achill |
| author_facet | Oertel, Alexander Schürmann, Achill |
| contents | Computing the copositive minimum of a strictly copositive quadratic form is a natural generalization of computing the arithmetical minimum of a positive definite one. In this paper we show that this generalized problem is NP-complete. Moreover, we describe a practical method to calculate all shortest vectors using the LDLT-decomposition in a big class of special cases. Our numerical tests show that our method performs significantly better than previous approaches. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_23696 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Computing the Copositive Minimum and its Representatives Oertel, Alexander Schürmann, Achill Number Theory Metric Geometry Optimization and Control 11H50 (Primary) 11Y16, 15A23, 90C20 (Secondary) Computing the copositive minimum of a strictly copositive quadratic form is a natural generalization of computing the arithmetical minimum of a positive definite one. In this paper we show that this generalized problem is NP-complete. Moreover, we describe a practical method to calculate all shortest vectors using the LDLT-decomposition in a big class of special cases. Our numerical tests show that our method performs significantly better than previous approaches. |
| title | On Computing the Copositive Minimum and its Representatives |
| topic | Number Theory Metric Geometry Optimization and Control 11H50 (Primary) 11Y16, 15A23, 90C20 (Secondary) |
| url | https://arxiv.org/abs/2509.23696 |