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A New H2 optimal model reduction method based on riemannian conjugate gradient method

In this paper, a new optimization problem formulation of the H2 optimal model reduction problem is introduced and discussed. The optimization problem is shown to be a problem on a product manifold, which is a Riemannian submanifold of a Euclidean space. Geometry of the resultant optimization problem is investigated and the Riemannian conjugate gradient method for the problem is proposed. Solutions obtained by the proposed method realize stable reduced order systems if the original system satisfies a certain condition, which holds for example for dissipative systems. It is shown by numerical experiments that the proposed method is effective for large-scale problems.