Structured Low-Rank Approximation as Optimization on a Grassmann Manifold

Many data modeling problems can be posed and solved as a structured low-rank approximation problem. Using the variable projection approach, the problem is reformulated as optimization on a Grassmann manifold. We compare local optimization methods based on different parametrizations of the manifold, including recently proposed penalty method and method of switching permutations. A numerical example of system identification is provided.