Parametric Semidefinite Programming: Geometry of the Trajectory of Solutions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913279971950592 |
|---|---|
| author | Bellon, Antonio Henrion, Didier Kungurtsev, Vyacheslav Marecek, Jakub |
| author_facet | Bellon, Antonio Henrion, Didier Kungurtsev, Vyacheslav Marecek, Jakub |
| contents | In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose coefficients (input data) depend on a time parameter. We are interested in the geometry of the solution (output data) trajectory, defined as the set of solutions depending on the parameter. We propose an exhaustive description of the geometry of the solution trajectory. As our main result, we show that only six distinct behaviors can be observed at a neighborhood of a given point along the solution trajectory. Each possible behavior is then illustrated by an example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_05445 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Parametric Semidefinite Programming: Geometry of the Trajectory of Solutions Bellon, Antonio Henrion, Didier Kungurtsev, Vyacheslav Marecek, Jakub Optimization and Control In many applications, solutions of convex optimization problems are updated on-line, as functions of time. In this paper, we consider parametric semidefinite programs, which are linear optimization problems in the semidefinite cone whose coefficients (input data) depend on a time parameter. We are interested in the geometry of the solution (output data) trajectory, defined as the set of solutions depending on the parameter. We propose an exhaustive description of the geometry of the solution trajectory. As our main result, we show that only six distinct behaviors can be observed at a neighborhood of a given point along the solution trajectory. Each possible behavior is then illustrated by an example. |
| title | Parametric Semidefinite Programming: Geometry of the Trajectory of Solutions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2104.05445 |