# Distributed Optimization on Riemannian Manifolds for multi-agent networks

arXiv: https://arxiv.org/abs/1711.11196 · HTML: https://mlsanity.com/paper/1711.11196/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Nov 2017.

## Built on by (most cited first, 5 of 5)

- [Decentralized Riemannian Gradient Descent on the Stiefel Manifold](https://mlsanity.com/paper/2102.07091/) (2021)
- [Federated Learning on Riemannian Manifolds](https://mlsanity.com/paper/2206.05668/) (2022)
- [Decentralized Riemannian Algorithm for Nonconvex Minimax Problems](https://mlsanity.com/paper/2302.03825/) (2023)
- [Decentralized Riemannian Conjugate Gradient Method on the Stiefel Manifold](https://mlsanity.com/paper/2308.10547/) (2023)
- [Decentralized Riemannian natural gradient methods with Kronecker-product approximations](https://mlsanity.com/paper/2303.09611/) (2023)

## Abstract (arXiv)

We consider the consensual distributed optimization problem in the Riemannian context. Specifically, the minimization of a sum of functions form is studied where each individual function in the sum is located at the node of a network. An algorithm, which is a direct generalization of the Euclidean case, to solve the problem is proposed. The convergence analysis is carried out in full detail for geodesically convex as well as non-convex functions. The algorithm is demonstrated using some standard applications which fit the presented framework.