This paper studies the convergence properties of the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple bound for the convergence rate is provided for message-passing. In comparison with previous results, our results do not require the given convex program to have known convex pairwise components and that our bound for the convergence rate is tighter and simpler. When specialised to quadratic optimisation, we generalise known results by providing a very simple bound for the convergence rate.

中文翻译：

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具有缩放对角线优势的分布式凸优化的消息传递算法的收敛性

本文研究了著名的用于凸优化的消息传递算法的收敛特性。在成对可分性和缩放对角线优势的假设下，建立了渐近收敛，并为消息传递提供了收敛速率的简单界限。与之前的结果相比，我们的结果不需要给定的凸程序具有已知的凸成对分量，并且我们对收敛速度的限制更严格和更简单。当专门用于二次优化时，我们通过为收敛速度提供一个非常简单的界限来概括已知结果。