Decentralized Riemannian

Decentralized Riemannian optimization focuses on solving optimization problems distributed across multiple agents, where the solution space is a Riemannian manifold—a curved space generalizing Euclidean space. Current research emphasizes developing efficient decentralized algorithms, such as variations of conjugate gradient and subgradient methods, often tailored to specific manifolds like the Stiefel manifold (used in applications involving orthogonal matrices). This area is significant because it enables scalable solutions for large-scale problems in machine learning (e.g., training neural networks) and other fields, overcoming limitations of centralized approaches by improving computational efficiency and robustness.