The Intrinsic Riemannian Proximal Gradient Method for Nonconvex Optimization

Ronny Bergmann; Hajg Jasa; Paula John; Max Pfeffer

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arXiv · 2506.09775

The Intrinsic Riemannian Proximal Gradient Method for Nonconvex Optimization

Ronny Bergmann·Hajg Jasa·Paula John·Max Pfeffer

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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.

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BibTeX RIS

Ronny Bergmann, Hajg Jasa, Paula John, Max Pfeffer. 2025-06-11. The Intrinsic Riemannian Proximal Gradient Method for Nonconvex Optimization. https://arxiv.org/abs/2506.09775

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