  We introduce the convex bundle method to solve convex, non-smooth
optimization problems on Riemannian manifolds. Each step of our method is based
on a model that involves the convex hull of previously collected subgradients,
parallely transported into the current serious iterate. This approach
generalizes the dual form of classical bundle subproblems in Euclidean space.
We prove that, under mild conditions, the convex bundle method converges to a
minimizer. Several numerical examples implemented using the Julia package
Manopt.jl illustrate the performance of the proposed method and compare it to
the subgradient method, the cyclic proximal point, as well as the proximal
bundle algorithm from Hoseini Monjezi, Nobakhtian, Pouryayevali, 2021.
