Novel shortcut strategies in copositivity detection: Decomposition for quicker positive certificates
Copositivity is a property of symmetric matrices which is NP-hard to check. Nevertheless, it plays a crucial role in tight bounds for conic approaches of several hard optimization problems. In this paper, we present novel promising shortcut strategies to exploit favorable instances in a systematic w...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2025-06-01
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| Series: | Operations Research Perspectives |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2214716024000289 |
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| Summary: | Copositivity is a property of symmetric matrices which is NP-hard to check. Nevertheless, it plays a crucial role in tight bounds for conic approaches of several hard optimization problems. In this paper, we present novel promising shortcut strategies to exploit favorable instances in a systematic way, using decomposition strategies based upon the idea to allow for overlapping, smaller blocks, profiting from a beneficial sign structure of the entries of the given matrix. The working hypothesis of this approach is the common empirical observation in the community that for detection of copositivity, a negative certificate is easier to obtain than a positive one. First empirical results on carefully orchestrated randomly generated instances seem to corroborate our approach. |
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| ISSN: | 2214-7160 |