Whitney Stratification of Algebraic Boundaries of Convex Semi-algebraic Sets
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917687461937152 |
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| author | Dai, Zihao Li, Zijia Yang, Zhi-Hong Zhi, Lihong |
| author_facet | Dai, Zihao Li, Zijia Yang, Zhi-Hong Zhi, Lihong |
| contents | Algebraic boundaries of convex semi-algebraic sets are closely related to polynomial optimization problems. Building upon Rainer Sinn's work, we refine the stratification of iterated singular loci to a Whitney (a) stratification, which gives a list of candidates of varieties whose dual is an irreducible component of the algebraic boundary of the dual convex body. We also present an algorithm based on Teissier's criterion to compute Whitney (a) stratifications, which employs conormal spaces and prime decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04681 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Whitney Stratification of Algebraic Boundaries of Convex Semi-algebraic Sets Dai, Zihao Li, Zijia Yang, Zhi-Hong Zhi, Lihong Optimization and Control Symbolic Computation Algebraic Geometry 52A99, 14N05, 14P10, 51N35, 14Q15 Algebraic boundaries of convex semi-algebraic sets are closely related to polynomial optimization problems. Building upon Rainer Sinn's work, we refine the stratification of iterated singular loci to a Whitney (a) stratification, which gives a list of candidates of varieties whose dual is an irreducible component of the algebraic boundary of the dual convex body. We also present an algorithm based on Teissier's criterion to compute Whitney (a) stratifications, which employs conormal spaces and prime decomposition. |
| title | Whitney Stratification of Algebraic Boundaries of Convex Semi-algebraic Sets |
| topic | Optimization and Control Symbolic Computation Algebraic Geometry 52A99, 14N05, 14P10, 51N35, 14Q15 |
| url | https://arxiv.org/abs/2406.04681 |