The Intrinsic Riemannian Proximal Gradient Method for Nonconvex Optimization
Optimization and Control
2025-06-12 v1 Numerical Analysis
Differential Geometry
Numerical Analysis
Abstract
We consider the proximal gradient method on Riemannian manifolds for functions that are possibly not geodesically convex. Starting from the forward-backward-splitting, we define an intrinsic variant of the proximal gradient method that uses proximal maps defined on the manifold and therefore does not require or work in the embedding. We investigate its convergence properties and illustrate its numerical performance, particularly for nonconvex or nonembedded problems that are hence out of reach for other methods.
Cite
@article{arxiv.2506.09775,
title = {The Intrinsic Riemannian Proximal Gradient Method for Nonconvex Optimization},
author = {Ronny Bergmann and Hajg Jasa and Paula John and Max Pfeffer},
journal= {arXiv preprint arXiv:2506.09775},
year = {2025}
}