Approximate Regularization Paths for Nuclear Norm Minimization using Singular Value Bounds: with Implementation and Extended Appendix

The widely used nuclear norm heuristic for rank minimizationproblems introduces a regularization parameter which isdifficult to tune. We have recently proposed a method to approximatethe regularization path, i.e., the optimal solution asa function of the parameter, which requires solving the problemonly for a sparse set of points. In this paper, we extendthe algorithm to provide error bounds for the singular valuesof the approximation. We exemplify the algorithms on largescale benchmark examples in model order reduction. Here,the order of a dynamical system is reduced by means of constrainedminimization of the nuclear norm of a Hankel matrix.