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.
A brief introduction to manifold op- timization
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A nonmonotone subgradient algorithm is developed for upper-C^2 optimization on submanifolds with stationarity and KL-based convergence guarantees.
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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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A Nonmonotone Descent Method for Optimization Problems Defined by Upper-$\mathcal{C}^2 $ Functions over Submanifolds
A nonmonotone subgradient algorithm is developed for upper-C^2 optimization on submanifolds with stationarity and KL-based convergence guarantees.