  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.
