@article{efficientoptimizationwithorthogonality, title = {Efficient Optimization with Orthogonality Constraint: a Randomized Riemannian Submanifold Method}, author = {Andi Han and Pierre-Louis Poirion and Akiko Takeda}, year = {2025}, eprint = {2505.12378}, archivePrefix = {arXiv}, url = {https://arxiv.org/abs/2505.12378v1}, }