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：当连通网络是一个直接图表时,梯度-推推算法被广泛用于分散优化问题。 本文显示,以 $\ alpha>0 的阶梯- 推推算法以指数速度快速地与优化器的美元( alpha) $( alpha) $- 邻里趋同, 假设每个成本均匀, 并且总成本非常高。 提供数值实验是为了支持理论趋同结果 。