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 penalty function for generalized orthogonality constraints matches first- and second-order stationary points of the original problem and runs faster than manifold optimization.
Introduces natural-gradient versions of Heavy-Ball and Nesterov momentum methods for function approximation on differentiable nonlinear manifolds.
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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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Improved Penalty Function Approaches for Optimization Problems with General Orthogonality
A penalty function for generalized orthogonality constraints matches first- and second-order stationary points of the original problem and runs faster than manifold optimization.
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Natural gradient descent with momentum
Introduces natural-gradient versions of Heavy-Ball and Nesterov momentum methods for function approximation on differentiable nonlinear manifolds.