A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
Computing Second- Order Points Under Equality Constraints: Revisiting Fletcher’s Augmented Lagrangian,
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Introduces the sketched landing method using Gaussian or subsampling sketch matrices to lower per-iteration cost in orthogonality-constrained optimization while preserving convergence guarantees in expectation.
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A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
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The sketched landing method for large-scale optimization under orthogonality constraints
Introduces the sketched landing method using Gaussian or subsampling sketch matrices to lower per-iteration cost in orthogonality-constrained optimization while preserving convergence guarantees in expectation.