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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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Geometric Design of the Tangent Term in Landing Algorithms for Orthogonality Constraints

  • 会议论文

  • 发表日期：

    2026年

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  • Florentin Goyens,
  • P.-A. Absil,
  • Florian Feppon

摘要

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.