Hardness of some optimization problems over correlation polyhedra
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914528417021952 |
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| author | Caprara, Alberto Furini, Fabio Gentile, Claudio Liberti, Leo Lodi, Andrea |
| author_facet | Caprara, Alberto Furini, Fabio Gentile, Claudio Liberti, Leo Lodi, Andrea |
| contents | We prove the \textbf{NP}-hardness, using Karp reductions, of some problems related to the correlation polytope and its corresponding cone, spanned by all of the $n\times n$ rank-one matrices over $\{0,1\}$. The problems are: membership, rank of the decomposition, and a ``relaxed rank'' obtained from relaxing the zero-norm expression for the rank to an $\ell_1$ norm. While membership and rank are natural problems for any matrix cone, the relaxed rank problem occurs in some signal processing and statistical applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02896 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hardness of some optimization problems over correlation polyhedra Caprara, Alberto Furini, Fabio Gentile, Claudio Liberti, Leo Lodi, Andrea Optimization and Control Computational Complexity We prove the \textbf{NP}-hardness, using Karp reductions, of some problems related to the correlation polytope and its corresponding cone, spanned by all of the $n\times n$ rank-one matrices over $\{0,1\}$. The problems are: membership, rank of the decomposition, and a ``relaxed rank'' obtained from relaxing the zero-norm expression for the rank to an $\ell_1$ norm. While membership and rank are natural problems for any matrix cone, the relaxed rank problem occurs in some signal processing and statistical applications. |
| title | Hardness of some optimization problems over correlation polyhedra |
| topic | Optimization and Control Computational Complexity |
| url | https://arxiv.org/abs/2605.02896 |