Consensus and balancing on the three-sphere
Consensus and balancing on the three-sphere
复制标题
三领域共识与平衡
DOI：
10.1007/s10898-018-0723-1
复制
发表时间：
2018
影响因子：
1.8
通讯作者：
V. Jaćimović
中科院分区：
文献类型：
--
作者：
Aladin Crnkić;V. Jaćimović
我们把3-球面上的一致性和反一致性问题作为全局优化问题来研究。相应的梯度下降算法是在一个动力系统上，即物理学中称为非阿贝尔的仓本模型.这一观察结果对以前的一些结果有了稍微不同的见解，也使我们能够证明一些关于完整图上的一致性和平衡性的新结果。这样我们就填补了现有理论中的一些空白。特别是，我们证明了反共识算法在完全图上收敛到一个平衡的配置，如果一个温和的条件，初始位置的代理是满足的。这个条件的形式表明与复分析中的一些重要构造有意想不到的关系。
We study consensus and anti-consensus on the 3-sphere as the global optimization problems. The corresponding gradient descent algorithm is a dynamical systems on, that is known in Physics asnon-Abelian Kuramoto model. This observation opens a slightly different insight into some previous results and also enables us to prove some novel results concerning consensus and balancing over the complete graph. In this way we fill some gaps in the existing theory. In particular, we prove that the anti-consensus algorithm over the complete graph onconverges towards a balanced configuration if a certain mild condition on initial positions of agents is satisfied. The form of this condition indicates an unexpected relation with some important constructions from Complex Analysis.