An nD-systems approach to global polynomial optimization with an application to H2 model order reduction

The problem of finding the global minimum of a multivariate polynomial can be approached by the matrix method of Stetter-Moller, which reformulates it as a large eigenvalue problem. The linear operators involved in this approach are studied using the theory of nD-systems. This supports the efficient application of iterative methods for solving eigenvalue problems such as Arnoldi methods and Jacobi-Davidson methods. This approach is demonstrated by an example which addresses optimal H2-model reduction of a linear dynamical model of order 10 to order 9. Index Terms: global polynomial optimization, Stetter-Moller matrix method, linear operator, nD-system, large eigenvalue problem, H2 model reductio