Iteration-complexity of gradient, subgradient and proximal point methods on Riemannian manifolds
Provides theoretical convergence guarantees for optimization on curved spaces, relevant for machine learning and optimization researchers working with non-Euclidean data.
The paper analyzes iteration-complexity bounds for gradient, subgradient, and proximal point methods on Riemannian manifolds, improving existing results for manifolds with non-negative curvature and Hadamard manifolds.
This paper considers optimization problems on Riemannian manifolds and analyzes iteration-complexity for gradient and subgradient methods on manifolds with non-negative curvature. By using tools from the Riemannian convex analysis and exploring directly the tangent space of the manifold, we obtain different iteration-complexity bounds for the aforementioned methods, complementing and improving related results. Moreover, we also establish iteration-complexity bound for the proximal point method on Hadamard manifolds.