Polynomial Optimization Over Unions of Sets
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914801405394944 |
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| author | Nie, Jiawang Zhang, Linghao |
| author_facet | Nie, Jiawang Zhang, Linghao |
| contents | This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove the asymptotic or finite convergence of the unified hierarchy. Special properties for the univariate case are discussed.The application for computing $(p,q)$-norms of matrices is also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17717 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polynomial Optimization Over Unions of Sets Nie, Jiawang Zhang, Linghao Optimization and Control This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove the asymptotic or finite convergence of the unified hierarchy. Special properties for the univariate case are discussed.The application for computing $(p,q)$-norms of matrices is also presented. |
| title | Polynomial Optimization Over Unions of Sets |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2404.17717 |