The algebraic degree of sparse polynomial optimization
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929380569120768 |
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| author | Lindberg, Julia Monin, Leonid Rose, Kemal |
| author_facet | Lindberg, Julia Monin, Leonid Rose, Kemal |
| contents | We study a broad class of polynomial optimization problems whose constraints and objective functions exhibit sparsity patterns. We give two characterizations of the number of critical points to these problems, one as a mixed volume and one as an intersection product on a toric variety. As a corollary, we obtain a convex geometric interpretation of polar degrees, a classical invariant of algebraic varieties, as well as Euclidean distance degrees. Furthermore, we prove the BKK generality of Lagrange systems in many instances. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_07765 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The algebraic degree of sparse polynomial optimization Lindberg, Julia Monin, Leonid Rose, Kemal Algebraic Geometry Optimization and Control 90C26, 14M25, 14Q20, 52B20 We study a broad class of polynomial optimization problems whose constraints and objective functions exhibit sparsity patterns. We give two characterizations of the number of critical points to these problems, one as a mixed volume and one as an intersection product on a toric variety. As a corollary, we obtain a convex geometric interpretation of polar degrees, a classical invariant of algebraic varieties, as well as Euclidean distance degrees. Furthermore, we prove the BKK generality of Lagrange systems in many instances. |
| title | The algebraic degree of sparse polynomial optimization |
| topic | Algebraic Geometry Optimization and Control 90C26, 14M25, 14Q20, 52B20 |
| url | https://arxiv.org/abs/2308.07765 |