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Parallelizable approaches for nonsmooth optimization problems with orthogonality constraints

摘要:In previous decades, the main step of the methods for optimization problems with orthogonality constraints is to search on the manifold or its tangent spaces, in which explicitly or implicitly orthonormalization procedure is inevitable so that the column-wise parallelization lacks of concurrency. Recently, we propose a few efficient infeasible approaches to solve this type of problems and demonstrate their potential in parallel computing. In this talk, we extend our approaches to a few nonsmooth cases. Problems like sparse variable principle component analysis, coordinate-independent sparse estimation can be solved in parallel with high scalability.