An algorithm for fast constrained nuclear norm minimization and applications to systems identification

This paper presents a novel algorithm for efficiently minimizing the nuclear norm of a matrix subject to structural and semi-definite constraints. It requires performing only thresholding and eigenvalue decomposition steps and converges Q-superlinearly to the optimum. Thus, this algorithm offers substantial advantages, both in terms of memory requirements and computational time over conventional semi-definite programming solvers. These advantages are illustrated using as an example the problem of finding the lowest order system that interpolates a collection of noisy measurements.