Global minimization of a multivariate polynomial using matrix methods

The problem of minimizing a polynomial function in several variables over ${bf R^n$ is considered and an algorithm is given. When the polynomial has a minimum the algorithm returns the global minimum and finds at least one point in every connected component of the set of minimizers. A characterization of such points is given. When the polynomial does not have a minimum the algorithm can compute its infimum. No assumption is made on the polynomial. The algorithm can be applied for solving a system of polynomial equations.