# Riemannian conditional gradient methods for composite optimization problems

arXiv: https://arxiv.org/abs/2412.19427 · HTML: https://mlsanity.com/paper/2412.19427/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Dec 2024.

## Built on by (most cited first, 1 of 1)

- [Geodesic Gradient Descent: A Generic and Learning-rate-free Optimizer on Objective Function-induced Manifolds](https://mlsanity.com/paper/2603.06651/) (2026)

## Abstract (arXiv)

In this paper, we propose Riemannian conditional gradient methods for minimizing composite functions, i.e., those that can be expressed as the sum of a smooth function and a retraction-based convex function. We analyze the convergence of the proposed algorithms, utilizing three types of step-size strategies: adaptive, diminishing, and those based on the Armijo condition. We establish the convergence rate of (O(1/k)) for the adaptive and diminishing step sizes, where (k) denotes the number of iterations. Additionally, we derive an iteration complexity of (O(1/ε2)) for the Armijo step-size strategy to achieve (ε)-optimality, where (ε) is the optimality tolerance. Finally, the effectiveness of our algorithms is validated through some numerical experiments performed on the sphere and Stiefel manifolds.