Sparse Polynomial Optimization with Unbounded Sets
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911766378708992 |
|---|---|
| author | Huang, Lei Kang, Shucheng Wang, Jie Yang, Heng |
| author_facet | Huang, Lei Kang, Shucheng Wang, Jie Yang, Heng |
| contents | This paper considers sparse polynomial optimization with unbounded sets. When the problem possesses correlative sparsity, we propose a sparse homogenized Moment-SOS hierarchy with perturbations to solve it. The new hierarchy introduces one extra auxiliary variable for each variable clique according to the correlative sparsity pattern. Under the running intersection property, we prove that this hierarchy has asymptotic convergence. Furthermore, we provide two alternative sparse hierarchies to remove perturbations while preserving asymptotic convergence. As byproducts, new Positivstellensätze are obtained for sparse positive polynomials on unbounded sets. Extensive numerical experiments demonstrate the power of our approach in solving sparse polynomial optimization problems on unbounded sets with up to thousands of variables. Finally, we apply our approach to tackle two trajectory optimization problems (block-moving with minimum work and optimal control of Van der Pol). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15837 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sparse Polynomial Optimization with Unbounded Sets Huang, Lei Kang, Shucheng Wang, Jie Yang, Heng Optimization and Control 90C23, 90C17, 90C22, 90C26 This paper considers sparse polynomial optimization with unbounded sets. When the problem possesses correlative sparsity, we propose a sparse homogenized Moment-SOS hierarchy with perturbations to solve it. The new hierarchy introduces one extra auxiliary variable for each variable clique according to the correlative sparsity pattern. Under the running intersection property, we prove that this hierarchy has asymptotic convergence. Furthermore, we provide two alternative sparse hierarchies to remove perturbations while preserving asymptotic convergence. As byproducts, new Positivstellensätze are obtained for sparse positive polynomials on unbounded sets. Extensive numerical experiments demonstrate the power of our approach in solving sparse polynomial optimization problems on unbounded sets with up to thousands of variables. Finally, we apply our approach to tackle two trajectory optimization problems (block-moving with minimum work and optimal control of Van der Pol). |
| title | Sparse Polynomial Optimization with Unbounded Sets |
| topic | Optimization and Control 90C23, 90C17, 90C22, 90C26 |
| url | https://arxiv.org/abs/2401.15837 |