Proximal bundle method achieves sublinear rates for general nonsmooth geodesically convex objectives and linear rates under sharp growth on Hadamard manifolds using only subgradients and inexact primitives.
Mifflin,An algorithm for constrained optimization with semismooth functions, Mathematics of Operations Research, 2 (1977), pp
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Nonsmooth Riemannian optimization with inexact manifold primitives via bundle methods
Proximal bundle method achieves sublinear rates for general nonsmooth geodesically convex objectives and linear rates under sharp growth on Hadamard manifolds using only subgradients and inexact primitives.