Distributed Optimization on Riemannian Manifolds for multi-agent networks

2017/11/29 by Suhail M. Shah, Shah, Suhail M. · 2 citations
Computer Science · Mathematics · #Distributed Control Multi-Agent Systems #FOS: Mathematics #Mathematical Biology Tumor Growth #Neural Networks Stability and Synchronization #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1711.11196

openalex publication_date 2017/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Distributed Riemannian Optimization in Geodesically Non-convex Environments
• Distributed Stochastic Proximal Algorithm on Riemannian Submanifolds for Weakly-convex Functions

Related

• Distributed Riemannian Optimization in Geodesically Non-convex Environments
• Distributed Stochastic Proximal Algorithm on Riemannian Submanifolds for Weakly-convex Functions
• Riemannian EXTRA: Communication-efficient decentralized optimization over compact submanifolds with data heterogeneity
• On the Linear Convergence of Distributed Optimization over Directed Graphs
• Consensus optimization on manifolds