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.

翻译：我们引入凸束方法以解决黎曼流形上的凸、非光滑优化问题。该方法每一步基于一个模型，该模型包含先前收集的次梯度的凸包，并平行传输至当前重要迭代点。此方法推广了欧氏空间中经典束子问题的对偶形式。我们证明，在温和条件下，凸束方法收敛至一个极小点。通过Julia包Manopt.jl实现的若干数值示例展示了所提出方法的性能，并将其与次梯度方法、循环近端点法以及Hoseini Monjezi、Nobakhtian、Pouryayevali（2021）的近端束算法进行了比较。