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arXiv · 2605.31505

The sketched landing method for large-scale optimization under orthogonality constraints

Florentin Goyens·Simon Mataigne·Pierre-Antoine Absil
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Abstract

We propose the sketched landing method, a randomized variant of the landing method for optimization under orthogonality constraints. Each landing step consists of the sum of a normal component, which reduces infeasibility, and a tangent component, which decreases the objective function. Our main contribution is the introduction of low-dimensional random 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.

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Florentin Goyens, Simon Mataigne, Pierre-Antoine Absil. 2026-05-29. The sketched landing method for large-scale optimization under orthogonality constraints. https://arxiv.org/abs/2605.31505

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