Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et. al., 2021], we present a convergence analysis of AMP dynamics with non-separable multivariate nonlinearities. As an application, we present a complete (and independent) analysis of the motivated convex optimization problem.

翻译：受近期近似消息传递（AMP）在多类分类中凸优化分析中的应用[Loureiro 等，2021]启发，本文对具有非分离多元非线性的AMP动力学进行了收敛性分析。作为应用，我们给出了所引出的凸优化问题的完整（且独立）分析。