ICLR 2026poster0 citations
Strongly Convex Sets in Riemannian Manifolds
Damien Scieur, David Martínez-Rubio, Thomas Kerdreux, Alexandre d'Aspremont, Sebastian Pokutta
Abstract
Strong convexity plays a key role in designing and analyzing convex optimization algorithms and is well-understood in Hilbert spaces. However, the notion of strongly convex sets beyond Hilbert spaces remains unclear. In this paper, we propose various definitions of strong convexity for uniquely geodesic sets in a Riemannian manifold, examine their relationships, introduce tools to identify geodesically strongly convex sets, and analyze the convergence of optimization algorithms over these sets. In particular, we show that the Riemannian Frank-Wolfe algorithm converges linearly when the Riemannian scaling inequalities hold.
Strong convexityRiemannianManifoldFrank-Wolfeoptimizationnonconvex
BibTeX
@inproceedings{
scieur2026strongly,
title={Strongly Convex Sets in Riemannian Manifolds},
author={Damien Scieur and David Mart{\'\i}nez-Rubio and Thomas Kerdreux and Alexandre d'Aspremont and Sebastian Pokutta},
booktitle={The Fourteenth International Conference on Learning Representations},
year={2026},
url={https://openreview.net/forum?id=4sDszSYKP6}
}