Geometric design of the tangent term in landing algorithms for orthogonality constraints

• URL: http://arxiv.org/abs/2507.15638v1
• Date: Mon, 21 Jul 2025 14:00:51 GMT
• Title: Geometric design of the tangent term in landing algorithms for orthogonality constraints
• Authors: Florentin Goyens, P. -A. Absil, Florian Feppon,
• Abstract summary: Family of metrics we propose is a natural extension of the $beta$-metric, defined on the Stiefel manifold.<n>Family of metrics we propose is a natural extension of the $beta$-metric, defined on the Stiefel manifold.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $\beta$-metric, defined on the Stiefel manifold.

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