Gradient-push algorithm has been widely used for decentralized optimization problems when the connectivity network is a direct graph. This paper shows that the gradient-push algorithm with stepsize $\alpha>0$ converges exponentially fast to an $O(\alpha)$-neighborhood of the optimizer under the assumption that each cost is smooth and the total cost is strongly convex. Numerical experiments are provided to support the theoretical convergence results.

翻译：梯度推送算法被广泛用于网络为有向图时的分散优化问题。本文表明，在假设每个代价函数光滑且总代价函数强凸的条件下，步长$\alpha>0$的梯度推送算法以指数速度收敛到优化器的$O(\alpha)$邻域内。提供的数值实验支持了理论收敛结果。