The sketched landing method for large-scale optimization under orthogonality constraints
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911733462859776 |
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| author | Goyens, Florentin Mataigne, Simon Absil, Pierre-Antoine |
| author_facet | Goyens, Florentin Mataigne, Simon Absil, Pierre-Antoine |
| contents | We propose the \emph{sketched landing method}, a randomized variant of the landing method for optimization under orthogonality constraints. Each landing step consists of the sum of a \emph{normal} component, which reduces infeasibility, and a \emph{tangent} component, which decreases the objective function. Our main contribution is the introduction of low-dimensional random \emph{sketch matrices} to reduce the computational cost of these directions. We consider both dense (Gaussian) and sparse (subsampling) sketch matrices, and show how they reduce the per-iteration cost while preserving convergence guarantees in expectation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31505 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The sketched landing method for large-scale optimization under orthogonality constraints Goyens, Florentin Mataigne, Simon Absil, Pierre-Antoine Optimization and Control 49M29 (primary), 53C21, 65K10, 90C30 (secondary) We propose the \emph{sketched landing method}, a randomized variant of the landing method for optimization under orthogonality constraints. Each landing step consists of the sum of a \emph{normal} component, which reduces infeasibility, and a \emph{tangent} component, which decreases the objective function. Our main contribution is the introduction of low-dimensional random \emph{sketch matrices} to reduce the computational cost of these directions. We consider both dense (Gaussian) and sparse (subsampling) sketch matrices, and show how they reduce the per-iteration cost while preserving convergence guarantees in expectation. |
| title | The sketched landing method for large-scale optimization under orthogonality constraints |
| topic | Optimization and Control 49M29 (primary), 53C21, 65K10, 90C30 (secondary) |
| url | https://arxiv.org/abs/2605.31505 |