Research
Retraction-Based Gradient Projection Algorithms on Manifolds
arXiv:2609.30885v1 Announce Type: cross Abstract: We introduce a framework for retraction-based convex optimization on Riemannian manifolds, which includes a notion of retraction-specific convex sets
arXiv:2609.30885v1 Announce Type: cross Abstract: We introduce a framework for retraction-based convex optimization on Riemannian manifolds, which includes a notion of retraction-specific convex sets and retraction-based gradient projection algorithms. The standard theory of gradient projection algorithms generalizes easily to this framework. Within this framework, we establish convergence results for retraction-based gradient projection algorithms with various stepsize rules. As an application, we use our framework to study the weighted low-rank approximation. We also provide numerical validation of our convergence results on the image completion task.
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Source: arXiv cs.LG | 2026-09-28