Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2406.06882 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909599230066688 |
|---|---|
| author | Nie, Jiawang Qu, Zheng Tang, Xindong Zhang, Linghao |
| author_facet | Nie, Jiawang Qu, Zheng Tang, Xindong Zhang, Linghao |
| contents | This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if the objective can be written as a sum of sparse nonnegative polynomials, each of which belongs to the sum of the ideal and quadratic module generated by the corresponding sparse constraints. Based on this characterization, we give several sufficient conditions for the sparse Moment-SOS hierarchy to be tight. In particular, we show that this sparse hierarchy is tight under some assumptions such as convexity, optimality conditions or finiteness of constraining sets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Characterization for Tightness of the Sparse Moment-SOS Hierarchy Nie, Jiawang Qu, Zheng Tang, Xindong Zhang, Linghao Optimization and Control This paper studies the sparse Moment-SOS hierarchy of relaxations for solving sparse polynomial optimization problems. We show that this sparse hierarchy is tight if and only if the objective can be written as a sum of sparse nonnegative polynomials, each of which belongs to the sum of the ideal and quadratic module generated by the corresponding sparse constraints. Based on this characterization, we give several sufficient conditions for the sparse Moment-SOS hierarchy to be tight. In particular, we show that this sparse hierarchy is tight under some assumptions such as convexity, optimality conditions or finiteness of constraining sets. |
| title | A Characterization for Tightness of the Sparse Moment-SOS Hierarchy |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2406.06882 |