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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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Operations Research Perspectives |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2214716024000289 |
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| author | Johannes Zischg Immanuel Bomze |
| author_facet | Johannes Zischg Immanuel Bomze |
| author_sort | Johannes Zischg |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-42bfa50163b34c78a3db6a2a6a218299 |
| institution | Kabale University |
| issn | 2214-7160 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Operations Research Perspectives |
| spelling | doaj-art-42bfa50163b34c78a3db6a2a6a2182992025-01-08T04:53:00ZengElsevierOperations Research Perspectives2214-71602025-06-0114100324Novel shortcut strategies in copositivity detection: Decomposition for quicker positive certificatesJohannes Zischg0Immanuel Bomze1Data Science @ Uni Vienna, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, AustriaCorresponding author.; Data Science @ Uni Vienna, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, AustriaCopositivity 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.http://www.sciencedirect.com/science/article/pii/S2214716024000289Nonconvex quadratic optimizationCopositive optimizationDecomposition |
| spellingShingle | Johannes Zischg Immanuel Bomze Novel shortcut strategies in copositivity detection: Decomposition for quicker positive certificates Operations Research Perspectives Nonconvex quadratic optimization Copositive optimization Decomposition |
| title | Novel shortcut strategies in copositivity detection: Decomposition for quicker positive certificates |
| title_full | Novel shortcut strategies in copositivity detection: Decomposition for quicker positive certificates |
| title_fullStr | Novel shortcut strategies in copositivity detection: Decomposition for quicker positive certificates |
| title_full_unstemmed | Novel shortcut strategies in copositivity detection: Decomposition for quicker positive certificates |
| title_short | Novel shortcut strategies in copositivity detection: Decomposition for quicker positive certificates |
| title_sort | novel shortcut strategies in copositivity detection decomposition for quicker positive certificates |
| topic | Nonconvex quadratic optimization Copositive optimization Decomposition |
| url | http://www.sciencedirect.com/science/article/pii/S2214716024000289 |
| work_keys_str_mv | AT johanneszischg novelshortcutstrategiesincopositivitydetectiondecompositionforquickerpositivecertificates AT immanuelbomze novelshortcutstrategiesincopositivitydetectiondecompositionforquickerpositivecertificates |