MADMM: A Generic Algorithm for Non-smooth Optimization on Manifolds

Artiom Kovnatsky, Klaus Glashoff, Michael M. Bronstein

Abstract: Numerous problems in computer vision, pattern recognition, and machine learning are formulated as optimization with manifold constraints. In this paper, we propose the Manifold Alternating Directions Method of Multipliers (MADMM), an extension of the classical ADMM scheme for manifold-constrained non-smooth optimization problems. To our knowledge, MADMM is the first generic non-smooth manifold optimization method. We showcase our method on several challenging problems in dimensionality reduction, non-rigid correspondence, multi-modal clustering, and multidimensional scaling.