Efficient Riemannian Inexact Augmented Lagrangian Method for Nonsmooth Composite Optimization on Manifolds

The proposed Riemannian inexact augmented Lagrangian (RiAL) method can find an ε-stationary point of a class of Riemannian nonsmooth composite problems with O(ε^-3) first-order oracle calls, achieving the best known oracle complexity.