Optimization on a Grassmann manifold with application to system identification

In this paper, we consider the problem of optimization of a cost function on a Grassmann manifold. This problem appears in system identification in the behavioral setting, which is a structured low-rank approximation problem. We develop a new method for local optimization on the Grassmann manifold with switching coordinate charts. This method reduces the optimization problem on the manifold to an optimization problem in a bounded domain of an Euclidean space. Our experiments show that this method is competitive with state- of-the-art retraction-based methods. Compared to retraction-based methods, the proposed method allows to incorporate easily an arbitrary optimization method for solving the optimization subproblem in the Euclidean space.