Second-order optimization on Stiefel manifold without retractions
A new second-order method for optimization on the Stiefel manifold achieves local quadratic convergence without using retractions. The update combines a tangent component to reduce the objective and a normal component to reduce infeasibility, constructed via Newton–Schulz iteration. The method offers a low-cost alternative to Riemannian approaches, with potential for high-accuracy requirements.
Key facts
- Method is second-order and retraction-free
- Local quadratic convergence proven
- Inexact variant achieves superlinear convergence
- Normal component uses Newton–Schulz fixed-point iteration
- Geometric connection established between Newton–Schulz and Stiefel manifolds
Entities
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