Solving clustered low-rank semidefinite programs arising from polynomial optimization
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909503615664128 |
|---|---|
| author | Leijenhorst, Nando de Laat, David |
| author_facet | Leijenhorst, Nando de Laat, David |
| contents | We study a primal-dual interior point method specialized to clustered low-rank semidefinite programs requiring high precision numerics, which arise from certain multivariate polynomial (matrix) programs through sums-of-squares characterizations and sampling. We consider the interplay of sampling and symmetry reduction as well as a greedy method to obtain numerically good bases and sample points. We apply this to the computation of three-point bounds for the kissing number problem, for which we show a significant speedup. This allows for the computation of improved kissing number bounds in dimensions $11$ through $23$. The approach performs well for problems with bad numerical conditioning, which we show through new computations for the binary sphere packing problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_12077 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Solving clustered low-rank semidefinite programs arising from polynomial optimization Leijenhorst, Nando de Laat, David Optimization and Control Metric Geometry 90C22, 90C23, 52C17, 90-04 We study a primal-dual interior point method specialized to clustered low-rank semidefinite programs requiring high precision numerics, which arise from certain multivariate polynomial (matrix) programs through sums-of-squares characterizations and sampling. We consider the interplay of sampling and symmetry reduction as well as a greedy method to obtain numerically good bases and sample points. We apply this to the computation of three-point bounds for the kissing number problem, for which we show a significant speedup. This allows for the computation of improved kissing number bounds in dimensions $11$ through $23$. The approach performs well for problems with bad numerical conditioning, which we show through new computations for the binary sphere packing problem. |
| title | Solving clustered low-rank semidefinite programs arising from polynomial optimization |
| topic | Optimization and Control Metric Geometry 90C22, 90C23, 52C17, 90-04 |
| url | https://arxiv.org/abs/2202.12077 |