On the optimal relaxation parameter of graph-based splitting methods for subspaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911568544923648 |
|---|---|
| author | Aragón-Artacho, Francisco J. López-Pastor, César |
| author_facet | Aragón-Artacho, Francisco J. López-Pastor, César |
| contents | In this paper, we investigate the behavior of the family of graph-based splitting algorithms specialized to the problem of finding a point in the intersection of linear subspaces. The algorithms in this family, which encompasses several classical methods such as the Douglas-Rachford algorithm, are defined by a connected graph and a subgraph. Our main result establishes that when the graph and subgraph coincide, the optimal relaxation parameter is exactly $1$, thereby extending known results for the Douglas-Rachford algorithm to a much broader class of methods. Our analysis hinges on some properties of iso-averaged linear operators, which are defined as the average of an isometry and the identity, and are characterized by a specific symmetry of the norm of their relaxation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04206 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the optimal relaxation parameter of graph-based splitting methods for subspaces Aragón-Artacho, Francisco J. López-Pastor, César Optimization and Control 65K05, 47N10, 47H09, 49M37, 90C25 In this paper, we investigate the behavior of the family of graph-based splitting algorithms specialized to the problem of finding a point in the intersection of linear subspaces. The algorithms in this family, which encompasses several classical methods such as the Douglas-Rachford algorithm, are defined by a connected graph and a subgraph. Our main result establishes that when the graph and subgraph coincide, the optimal relaxation parameter is exactly $1$, thereby extending known results for the Douglas-Rachford algorithm to a much broader class of methods. Our analysis hinges on some properties of iso-averaged linear operators, which are defined as the average of an isometry and the identity, and are characterized by a specific symmetry of the norm of their relaxation. |
| title | On the optimal relaxation parameter of graph-based splitting methods for subspaces |
| topic | Optimization and Control 65K05, 47N10, 47H09, 49M37, 90C25 |
| url | https://arxiv.org/abs/2604.04206 |