Manifold Proximal Point Algorithms for Dual Principal Component Pursuit and Orthogonal Dictionary Learning

Dual principal component pursuit and orthogonal dictionary learning are two fundamental tools in data analysis, and both of them can be formulated as a manifold optimization problem with nonsmooth objective. Algorithms with convergence guarantees for solving this kind of problems have been very limited in the literature. In this paper, we propose a novel manifold proximal point algorithm for solving this nonsmooth manifold optimization problem. Numerical results are reported to demonstrate the effectiveness of the proposed algorithm.