{"ID":2864190,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.23696","arxiv_id":"2509.23696","title":"On Computing the Copositive Minimum and its Representatives","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.23696","url_pdf":"https://arxiv.org/pdf/2509.23696v1","authors":"[\"Alexander Oertel\",\"Achill Schürmann\"]","published":"2025-09-28T07:08:38Z","proceeding":"math.NT","tasks":"[\"math.NT\",\"math.MG\",\"math.OC\"]","methods":"[]","has_code":false}