In this paper, we generalize proximal methods that were originally designed for convex optimization on normed vector space to non-convex pose graph optimization (PGO) on special Euclidean groups, and show that our proposed generalized proximal methods for PGO converge to first-order critical points. Furthermore, we propose methods that significantly accelerate the rates of convergence almost without loss of any theoretical guarantees. In addition, our proposed methods can be easily distributed and parallelized with no compromise of efficiency. The efficacy of this work is validated through implementation on simultaneous localization and mapping (SLAM) and distributed 3D sensor network localization, which indicate that our proposed methods are a lot faster than existing techniques to converge to sufficient accuracy for practical use.

翻译：在本文中,我们将最初为规范矢量空间的优化而设计的近似方法推广为非convex为特殊欧几里德群体提供图形优化,并表明我们提议的PGO通用近似方法与第一级临界点趋同。此外,我们建议的方法几乎在不丧失任何理论保证的情况下大大加快了趋同速度。此外,我们提出的方法可以容易地分布和平行,而不会损及效率。这项工作的效力通过同时进行本地化和绘图(SLAM)和分布式三维传感器网络本地化得到验证,这表明我们所提议的方法比现有技术要快得多,足以达到实际使用的足够准确性。