Retraction-Based Gradient Projection Algorithms on Manifolds

The paper presents a framework for retraction-based convex optimization on Riemannian manifolds, introducing retraction-specific convex sets and retraction-based gradient projection algorithms. It extends the standard theory of gradient projection algorithms to this setting and proves convergence results for various stepsize rules. The authors apply the framework to weighted low-rank approximation and validate the convergence results numerically on an image completion task.

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