Retraction-Based Gradient Projection Algorithms on Manifolds

arXiv:2609.30885 · math.OC, cs.LG · Submitted 2026-09-25 · Read on arXiv

math.OC, cs.LG

Submitted: 2026-09-25

Updated: 2026-09-25

Code: https://github.com/ConglongXu-GWU/manifold-grad-proj-release

Terminology

• Benchmark — 47× in this paper · explained in 2 episodes
• Regularization — 21× in this paper · explained in 3 episodes
• Stiefel manifold — 14× in this paper · explained in 2 episodes
• Matrix Completion — 11× in this paper · explained in 3 episodes
• Riemannian optimization — 7× in this paper · explained in 2 episodes
• Core — 4× in this paper · explained in 2 episodes
• Objective Function — 4× in this paper · explained in 2 episodes
• Accuracy — 2× in this paper · explained in 1 episode
• Adaptation — 2× in this paper · explained in 1 episode
• Degeneracy — 2× in this paper · explained in 3 episodes
• Differentially Private — 1× in this paper · explained in 3 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Provenance — 1× in this paper · explained in 3 episodes

Sources

• Regularized Weighted Low Rank Approximation
• Geodesic Convex Optimization: Differentiation on Manifolds, Geodesics, and Convexity
• Weighted Low-rank Approximation via Stochastic Gradient Descent on Manifolds

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