Reviews: A Linearly Convergent Method for Non-Smooth Non-Convex Optimization on the Grassmannian with Applications to Robust Subspace and Dictionary Learning

A number of problems in sparse learning, signal processing, etc., can be phrased as optimizing a nonsmooth function over a riemannian manifold. Many works avoid nonsmooth analysis / optimization, by applying smooth methods to a smoothing of the objective function, often at the cost of suboptimalities in convergence rate, sample complexity, etc.. This work takes a different path, directly developing methods for nonsmooth riemannian optimization. The focus on the grassmannian limits the scope to some extent. It is unclear what in the setup requires the grassmannian.