{"ID":2892281,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.15638","arxiv_id":"2507.15638","title":"Geometric design of the tangent term in landing algorithms for orthogonality constraints","abstract":"We propose a family a metrics over the set of full-rank $n\\times p$ real matrices, and apply them to the landing framework for optimization under orthogonality constraints. The family of metrics we propose is a natural extension of the $β$-metric, defined on the Stiefel manifold.","short_abstract":"We propose a family a metrics over the set of full-rank $n\\times p$ real matrices, and apply them to the landing framework for optimization under orthogonality constraints. The family of metrics we propose is a natural extension of the $β$-metric, defined on the Stiefel manifold.","url_abs":"https://arxiv.org/abs/2507.15638","url_pdf":"https://arxiv.org/pdf/2507.15638v1","authors":"[\"Florentin Goyens\",\"P. -A. Absil\",\"Florian Feppon\"]","published":"2025-07-21T14:00:51Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"stat.ML\"]","methods":"[]","has_code":false}