## Distributed heavy-ball: A generalization and acceleration of first-order methods with gradient tracking. (arXiv:1808.02942v1 [math.OC])

We study distributed optimization to minimize a global objective that is a
sum of smooth and strongly-convex local cost functions. Recently, several
algorithms over undirected and directed graphs have been proposed that use a
gradient tracking method to achieve linear convergence to the global minimizer.
However, a connection between these different approaches has been unclear. In
this paper, we first show that many of the existing first-order algorithms are
in fact related with a simple state transformation, at the heart of which lies
the~$\mc{AB}$ algorithm. We then describe \textit{distributed heavy-ball},
denoted as~$\mc{AB}m$, i.e.,~$\mc{AB}$ with momentum, that combines gradient
tracking with a momentum term and uses nonidentical local step-sizes.
By~simultaneously implementing both row- and column-stochastic
weights,~$\mc{AB}m$ removes the conservatism in the related work due to
doubly-stochastic weights or eigenvector estimation.~$\mc{AB}m$ thus naturally
leads to optimization查看全文