In this paper, we consider networks with topologies described by some connected undirected graph ${\mathcal{G}}=(V, E)$ and with some agents (fusion centers) equipped with processing power and local peer-to-peer communication, and optimization problem $\min_{{\boldsymbol x}}\big\{F({\boldsymbol x})=\sum_{i\in V}f_i({\boldsymbol x})\big\}$ with local objective functions $f_i$ depending only on neighboring variables of the vertex $i\in V$. We introduce a divide-and-conquer algorithm to solve the above optimization problem in a distributed and decentralized manner. The proposed divide-and-conquer algorithm has exponential convergence, its computational cost is almost linear with respect to the size of the network, and it can be fully implemented at fusion centers of the network. Our numerical demonstrations also indicate that the proposed divide-and-conquer algorithm has superior performance than popular decentralized optimization methods do for the least squares problem with/without $\ell^1$ penalty.
翻译：在本文中,我们考虑一些未连接的图形 $_mathcal{G}{(V,E) 所描述的具有地形学的网络,有些未连接的图形 $_mathcal{G}}(V,E) 和一些配有处理力和地方同行通信的代理商(聚变中心)所描述的网络,以及优化问题 $\min ⁇ boldsymbol x ⁇ big}F ({boldsymbol x})\\ f_i (boldsysymbol x})\ f_i)\ big $(boldsymball x})\ big $\ big $($f_i) $(i) $(i) $(i) $(i) $(i) ) 美元(i) 美元(i) 。 我们采用分流和分散化算法来解决上述优化问题。提议的分化算法具有指数的计算成本与网络的大小几乎是线性, 可以在网络的聚变数中心完全执行。 我们的数字演示还表明, 提议的分化算算算算算法比流行的比分散化法的比分散化法在最小平方问题时, 用/不以/ $\\ $\\\\ $\ $\ $\ $\ $\\\ $ $ $ $ $ $ $ $ $ $ $ $ $ $ = $ $ $ = $ $ = = = $ $ $ = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
相关内容
微信扫码咨询专知VIP会员