Consensus optimization on manifolds
| dc.creator | Sarlette, Alain | |
| dc.creator | Sepulchre, Rodolphe | |
| dc.date | 2008-11-26 | |
| dc.date.accessioned | 2026-07-07T12:04:31Z | |
| dc.date.available | 2026-07-07T12:04:31Z | |
| dc.description | The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e. maximizing the consensus) or balance (i.e. minimizing the consensus) the agents; a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time-varying. The cost function is linked to a specific centroid definition on manifolds, introduced here as the induced arithmetic mean, that is easily computable in closed form and may be of independent interest for a number of manifolds. The special orthogonal group SO(n) and the Grassmann manifold Gr(p,n) are treated as original examples. A link is also drawn with the many existing results on the circle. | |
| dc.description | Preprint submitted to SIAM/SICON September 2006; revised November 2007; accepted for publication April 2008; publication date unknown before 2009 | |
| dc.identifier | https://arxiv.org/abs/0811.4275 | |
| dc.identifier | http://arxiv.org/abs/0811.4275 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208155 | |
| dc.subject | Optimization and Control | |
| dc.subject | Differential Geometry | |
| dc.title | Consensus optimization on manifolds | |
| dc.type | text |