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The widely used nuclear norm heuristic for rank minimization problemsintroduces a regularization parameter which is difficult to tune. We haverecently proposed a method to approximate the regularization path, i.e., theoptimal solution as a function of the parameter, which requires solving theproblem only for a sparse set of points. In this paper, we extend the algorithmto provide error bounds for the singular values of the approximation. Weexemplify the algorithms on large scale benchmark examples in model orderreduction. Here, the order of a dynamical system is reduced by means ofconstrained minimization of the nuclear norm of a Hankel matrix.

Approximate Regularization Paths for Nuclear Norm Minimization Using Singular Value Bounds -- With Implementation and Extended Appendix